Matrices Class 12 MCQ Online Test With Answers Questions

Check the below NCERT MCQ Questions for Class 12 Maths Chapter 3 Matrices with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Matrices Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

Class 12 Maths Chapter 3 MCQ With Answers

Maths Class 12 Chapter 3 MCQs On Matrices

Matrices Class 12 MCQ Questions Chapter 3 Question 1.
\(\left|\begin{array}{lll}
3 & 4 & 5 \\
0 & 2 & 3 \\
0 & 0 & 7
\end{array}\right|\) = A then |A| = ?
(a) 40
(b) 50
(c) 42
(d) 15

Answer

Answer: (c) 42

Matrices Class 12 MCQ Chapter 3 Question 2.
The inverse of A = \(\left|\begin{array}{ll}
2 & 3 \\
5 & k
\end{array}\right|\) will not be obtained if A has the value
(a) 2
(b) \(\frac{3}{2}\)
(c) \(\frac{5}{2}\)
(d) \(\frac{15}{2}\)

Answer

Answer: (d) \(\frac{15}{2}\)

Matrices MCQ Questions Class 12 Question 3.
For any unit matrix I
(a) I² = I
(b) |I| = 0
(c) |I| = 2
(d) |I| = 5

Answer

Answer: (a) I² = I

Matrix Class 12 MCQ Chapter 3 Question 4.
A matrix A = [a_ij]_m×n is said to be symmetric if
(a) a_ij = 0
(b) a_ij = a_ji
(c) a_ij = a_ij
(d) a_ij = 1

Answer

Answer: (b) a_ij = a_ji

Class 12 Maths Chapter 3 MCQ Question 5.
If A = \(\left|\begin{array}{lll}
1 & 1 & 1 \\
1 & 1 & 1 \\
1 & 1 & 1
\end{array}\right|\) then A² is
(a) 27 A
(b) 2 A
(c) 3 A
(d) 1

Answer

Answer: (c) 3 A

MCQ Of Matrices Class 12 Question 6.
A matrix A = [a_ij]_m×n is said to be skew symmetric if
(a) a_ij = 0
(b) a_ij = a_ji
(c) a_ij = -a_ji
(d) a_ij = 1

Answer

Answer: (b) a_ij = a_ji

Matrices MCQ Class 12 Chapter 3 Question 7.
A = [a_ij]_m×n is a square matrix if
(a) m = n
(b) m < n
(c) m > n
(d) None of these

Answer

Answer: (a) m = n

Matrix MCQ Class 12 Chapter 3 Question 8.
If A and B are square matrices then (AB)’ =
(a) B’A’
(b) A’B’
(c) AB’
(d) A’B’

Answer

Answer: (a) B’A’

MCQ On Matrices Class 12 Chapter 3 Question 9.
If A = \(\left[\begin{array}{cc}
\cos \theta & -\sin \theta \\
\sin \theta & \cos \theta
\end{array}\right]\) and adj A is
(a) \(\left[\begin{array}{cc}
\cos \theta & -\sin \theta \\
\sin \theta & \cos \theta
\end{array}\right]\)
(b) \(\left[\begin{array}{cc}
1 & 0 \\
0 & 1
\end{array}\right]\)
(c) \(\left[\begin{array}{cc}
\cos \theta & \sin \theta \\
-\sin \theta & \cos \theta
\end{array}\right]\)
(d) \(\left[\begin{array}{cc}
-1 & 0 \\
0 & -1
\end{array}\right]\)

Answer

Answer: (c) \(\left[\begin{array}{cc}
\cos \theta & \sin \theta \\
-\sin \theta & \cos \theta
\end{array}\right]\)

Class 12 Matrices MCQ Chapter 3 Question 10.
If \(\left[\begin{array}{cc}
1-x & 2 \\
18 & 6
\end{array}\right]\) = \(\left[\begin{array}{cc}
6 & 2 \\
18 & 6
\end{array}\right]\) then x =
(a) ±6
(b) 6
(c) -5
(d) 7

Answer

Answer: (c) -5

Matrix MCQ Questions Chapter 3 Question 11.
If \(\left|\begin{array}{ll}
x & 8 \\
3 & 3
\end{array}\right|\) = 0, the value of x is
(a) 3
(b) 8
(c) 24
(d) 0

Answer

Answer: (b) 8

MCQ Of Matrix Class 12 Chapter 3 Question 12.
If A = \(\left[\begin{array}{cc}
i & 0 \\
0 & i
\end{array}\right]\) then A² =
(a) \(\left[\begin{array}{cc}
1 & 0 \\
0 & -1
\end{array}\right]\)
(b) \(\left[\begin{array}{cc}
-1 & 0 \\
0 & -1
\end{array}\right]\)
(c) \(\left[\begin{array}{cc}
1 & 0 \\
0 & 1
\end{array}\right]\)
(d) \(\left[\begin{array}{cc}
-1 & 0 \\
0 & 1
\end{array}\right]\)

Answer

Answer: (b) \(\left[\begin{array}{cc}
-1 & 0 \\
0 & -1
\end{array}\right]\)

Matrices MCQ With Answers Pdf Chapter 3 Question 13.
Let A be a non-singular matrix of the order 2 × 2 then |A^-1|=
(a) |A|
(b) \(\frac{1}{|A|}\)
(c) 0
(d) 1

Answer

Answer: (b) \(\frac{1}{|A|}\)

MCQ On Matrices Class 12 Pdf Download Question 14.
If A = \(\left[\begin{array}{cc}
1 & 2 \\
2 & 1
\end{array}\right]\) then adj A =
(a) \(\left[\begin{array}{cc}
1 & -2 \\
-2 & 1
\end{array}\right]\)
(b) \(\left[\begin{array}{cc}
2 & 1 \\
1 & 1
\end{array}\right]\)
(c) \(\left[\begin{array}{cc}
1 & -2 \\
-2 & -1
\end{array}\right]\)
(d) \(\left[\begin{array}{cc}
-1 & 2 \\
-2 & -1
\end{array}\right]\)

Answer

Answer: (a) \(\left[\begin{array}{cc}
1 & -2 \\
-2 & 1
\end{array}\right]\)

Class 12 Matrix MCQ Questions Chapter 3 Question 15.
If A = \(\left[\begin{array}{cc}
1 & 1 \\
0 & 1
\end{array}\right]\) B = \(\left[\begin{array}{cc}
0 & 1 \\
1 & 0
\end{array}\right]\) then AB =
(a) \(\left[\begin{array}{cc}
0 & 0 \\
0 & 0
\end{array}\right]\)
(b) \(\left[\begin{array}{cc}
1 & 1 \\
1 & 0
\end{array}\right]\)
(c) \(\left[\begin{array}{cc}
1 & 0 \\
0 & 1
\end{array}\right]\)
(d) 10

Answer

Answer: (b) \(\left[\begin{array}{cc}
1 & 1 \\
1 & 0
\end{array}\right]\)

Matrices Class 12 MCQs Chapter 3 Question 16.
If \(\left[\begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
a & b & -1
\end{array}\right]\) then A² =
(a) a unit matrix
(b) A
(c) a null matrix
(d) -A

Answer

Answer: (a) a unit matrix

Chapter 3 Maths Class 12 MCQ Question 17.
If A = \(\left[\begin{array}{cc}
α & 0 \\
1 & 1
\end{array}\right]\) B = \(\left[\begin{array}{cc}
1 & 0 \\
5 & 1
\end{array}\right]\) where A² = B then the value of α is
(a) 1
(b) -1
(c) 4
(d) we cant calculate the value of α

Answer

Answer: (d) we cant calculate the value of α

Class 12 Maths Ch 3 MCQ Question 18.
If A = \(\left[\begin{array}{cc}
1 & 2 \\
3 & 4
\end{array}\right]\) then
(a) |A| = 0
(b) A^-1 exists
(c) A^-1 does not exist
(d) None of these

Answer

Answer: (b) A^-1 exists

MCQ Class 12 Maths Chapter 3 Question 19.
If A = \(\left[\begin{array}{cc}
2x & 5 \\
8 & x
\end{array}\right]\) = \(\left[\begin{array}{cc}
6 & -2 \\
7 & 3
\end{array}\right]\) then the value of x is
(a) 3
(b) ±3
(c) ±6
(d) 6

Answer

Answer: (a) 3

Matrix MCQ Questions And Answers Chapter 3 Question 20.
Let A = \(\left[\begin{array}{cc}
1 & -1 \\
2 & 3
\end{array}\right]\) then
(a) A^-1 = \(\left[\begin{array}{cc}
\frac{3}{5} & \frac{1}{5} \\
\frac{-2}{5} & \frac{1}{5}
\end{array}\right]\)
(b) |A| = 0
(c) |A| = 5
(d) A² = 1

Answer

Answer: (a) A^-1 = \(\left[\begin{array}{cc}
\frac{3}{5} & \frac{1}{5} \\
\frac{-2}{5} & \frac{1}{5}
\end{array}\right]\)

Question 21.
If A = \( \left[\begin{array}{ccc}
2 & \lambda & -3 \\
0 & 2 & 5 \\
1 & 1 & 3
\end{array}\right]\) yhen A^-1 exists if
(a) λ = 2
(b) λ ≠ 2
(c) λ ≠ -2
(d) none of these

Answer

Answer: (d) none of these

Question 22.
If A = \(\left[\begin{array}{cc}
α & 2 \\
2 & α
\end{array}\right]\) and |A³| = 25 then α is
(a) ±3
(b) ±2
(c) ±5
(d) 0

Answer

Answer: (a) ±3

Question 23.
A² – A + I = 0 then the inverse of A
(a) A
(b) A + I
(c) I – A
(d) A – I

Answer

Answer: (c) I – A

Question 24.
If A = \(\left[\begin{array}{cc}
2 & 3 \\
1 & -4
\end{array}\right]\) and B = \(\left[\begin{array}{cc}
1 & -2 \\
-1 & 3
\end{array}\right]\) then find (AB)^-1
(a) \(\frac{1}{11}\) \(\left[\begin{array}{cc}
14 & 5 \\
5 & 1
\end{array}\right]\)
(b) \(\frac{1}{11}\) \(\left[\begin{array}{cc}
14 & -5 \\
-5 & 1
\end{array}\right]\)
(c) \(\frac{1}{11}\) \(\left[\begin{array}{cc}
1 & 5 \\
5 & 14
\end{array}\right]\)
(d) \(\frac{1}{11}\) \(\left[\begin{array}{cc}
1 & -5 \\
-5 & 14
\end{array}\right]\)

Answer

Answer: (a) \(\frac{1}{11}\) \(\left[\begin{array}{cc}
14 & 5 \\
5 & 1
\end{array}\right]\)

Question 25.
If A = \(\left[\begin{array}{cc}
3 & 1 \\
-1 & 2
\end{array}\right]\) then A² – 5A – 7I is
(a) zero matrix
(b) a diagonal matrix
(c) identity matrix
(d) None of these

Answer

Answer: (b) a diagonal matrix

Question 26.
If A = \(\left[\begin{array}{cc}
\cos x & -\sin x \\
\sin x & \cos x
\end{array}\right]\) then A + A^T = I if the value of x is
(a) \(\frac{π}{6}\)
(b) \(\frac{π}{3}\)
(c) π
(d) 0

Answer

Answer: (b) \(\frac{π}{3}\)

Question 27.
If \(\left[\begin{array}{cc}
x+y & y \\
2x & x-y
\end{array}\right]\) \(\left[\begin{array}{c}
2 \\
-1
\end{array}\right]\) \(\left[\begin{array}{c}
3 \\
2
\end{array}\right]\) then xy equal to
(a) -5
(b) -4
(c) 4
(d) 5

Answer

Answer: (a) -5

Question 28.
If A = \(\left[\begin{array}{cc}
1 & 2 \\
4 & 2
\end{array}\right]\) then |2A| =
(a) 2|A|
(b) 4|A|
(c) 8|A|
(d) None of these

Answer

Answer: (b) 4|A|

Question 29.
If A = \(\left[\begin{array}{cc}
a & b \\
c & d
\end{array}\right]\) then A² is equal to
(a) \(\left[\begin{array}{cc}
a^{2} & b^{2} \\
c^{2} & d^{2}
\end{array}\right]\)
(b) \(\left[\begin{array}{cc}
b^{2}+bc & ab+bd \\
ac+dc & dc+d^{2}
\end{array}\right]\)
(c) \(\left[\begin{array}{cc}
a^{3} & b^{3} \\
c^{3} & d^{3}
\end{array}\right]\)
(d) None of these

Answer

Answer: (b) \(\left[\begin{array}{cc}
b^{2}+bc & ab+bd \\
ac+dc & dc+d^{2}
\end{array}\right]\)

Question 30.
\(\left[\begin{array}{cc}
\cos \theta & -\sin \theta \\
-\sin \theta & \cos \theta
\end{array}\right]\) is inverse of
(a) \(\left[\begin{array}{cc}
-\cos \theta & -\sin \theta \\
-\sin \theta & \cos \theta
\end{array}\right]\)
(b) \(\left[\begin{array}{cc}
\cos \theta & \sin \theta \\
\sin \theta & -\cos \theta
\end{array}\right]\)
(c) \(\left[\begin{array}{cc}
\cos \theta & \sin \theta \\
-\sin \theta & \cos \theta
\end{array}\right]\)
(d) None of these

Answer

Answer: (c) \(\left[\begin{array}{cc}
\cos \theta & \sin \theta \\
-\sin \theta & \cos \theta
\end{array}\right]\)

Question 31.
A = \(\left[\begin{array}{cc}
a & b \\
b & a
\end{array}\right]\) and A² = \(\left[\begin{array}{cc}
α & β \\
β & α
\end{array}\right]\) then
(a) α = a² + b², β = ab
(b) α = a² + b², β = 2ab
(c) α = a² + b², β = a² – b²
(d) α = 2ab, β = a² + b²

Answer

Answer: (b) α = a² + b², β = 2ab

Question 32.
The matrix \(\left[\begin{array}{ccc}
2 & -1 & 4 \\
1 & 0 & -5 \\
-4 & 5 & 7
\end{array}\right]\) is
(a) a symmetric matix
(b) a skew-sybtmetric matrix
(c) a diagonal matrix
(d) None of these

Answer

Answer: (d) None of these

Question 33.
If a matrix is both symmetric matrix and skew symmetric matrix then
(a) A is a diagonal matrix
(b) A is zero matrix
(c) A is scalar matrix
(d) None of these

Answer

Answer: (b) A is zero matrix

Question 34.
If \(\left[\begin{array}{cc}
x+y & 3 \\
4 & x-y
\end{array}\right]\) = \(\left[\begin{array}{cc}
1 & 3 \\
4 & -3
\end{array}\right]\) then (x, y) is
(a) (-1, 2)
(b) (-1, -2)
(c) (-2, -1)
(d) (1, -2)

Answer

Answer: (a) (-1, 2)

Question 35.
The matrix P = \(\left[\begin{array}{ccc}
0 & 0 & 4 \\
0 & 4 & 0 \\
4 & 0 & 0
\end{array}\right]\) is
(a) square matrix
(b) diagonal matrix
(c) unit matrix
(d) None of these

Answer

Answer: (a) square matrix

Question 36.
Total number of possible matrices of order 3 × 3 with each entry 2 or 0 is
(a) 9
(b) 27
(c) 81
(d) 512

Answer

Answer: (d) 512

Question 37.
If \(\left[\begin{array}{cc}
2x+y & 4x \\
5x-7 & 4x
\end{array}\right]\) = \(\left[\begin{array}{cc}
7 & 7y-13 \\
y & x+6
\end{array}\right]\) then the value of x, y is
(a) 3, 1
(b) 2, 3
(c) 2, 4
(d) 3, 3

Answer

Answer: (b) 2, 3

Question 38.
If A and B are two matrices of the order 3 × m and 3 × n, respectively, and m = n, then the order of matrix (5A – 2B) is
(a) m × 3
(b) 3 × 3
(c) m × n
(d) 3 × n

Answer

Answer: (d) 3 × n

Question 39.
If A = \(\frac{1}{π}\) \(\left[\begin{array}{cc}
\sin ^{-1}(x \pi) & \tan^{1}\left(\frac{x}{\pi}\right) \\
\sin ^{-1}\left(\frac{x}{\pi}\right) & \cot ^{-1}(\pi x)
\end{array}\right]\)
B = \(\frac{1}{π}\) \(\left[\begin{array}{cc}
\cos ^{-1}(x \pi) & \tan ^{-1}\left(\frac{x}{\pi}\right) \\
\sin ^{-1}\left(\frac{x}{\pi}\right) & -\tan ^{-1}(\pi x)
\end{array}\right]\)
then A – B equal to
(a) I
(b) O
(c) 1
(d) \(\frac{3}{2}\) I

Answer

Answer: (d) \(\frac{3}{2}\) I

Question 40.
If A = \(\left[\begin{array}{cc}
0 & 1 \\
1 & 0
\end{array}\right]\) then A² is equal to
(a) \(\left[\begin{array}{cc}
0 & 1 \\
1 & 0
\end{array}\right]\)
(b) \(\left[\begin{array}{cc}
1 & 0 \\
1 & 0
\end{array}\right]\)
(c) \(\left[\begin{array}{cc}
0 & 1 \\
0 & 1
\end{array}\right]\)
(d) \(\left[\begin{array}{cc}
1 & 0 \\
0 & 1
\end{array}\right]\)

Answer

Answer: (d) \(\left[\begin{array}{cc}
1 & 0 \\
0 & 1
\end{array}\right]\)

Question 41.
If matrix A = [a_ij]_2×2 where a_ij = {\(_{0 if i = j}^{1 if i ≠ j}\) then A² is equal to
(a) I
(b) A
(c) O
(d) None of these

Answer

Answer: (a) I

Question 42.
The matrix \(\left[\begin{array}{ccc}
1 & 0 & 0 \\
0 & 2 & 0 \\
0 & 0 & 0
\end{array}\right]\) is a
(a) identity matrix
(b) symmetric matrix
(c) skew symmetric matrix
(d) None of these

Answer

Answer: (b) symmetric matrix

Question 43.
The matrix \(\left[\begin{array}{ccc}
0 & -5 & 8 \\
5 & 0 & 12 \\
-8 & -12 & 0
\end{array}\right]\) is a
(a) diagonal matrix
(b) symmetric matrix
(c) skew symmetric matrix
(d) scalar matrix

Answer

Answer: (c) skew symmetric matrix

Question 44.
If A is matrix of order m × n and B is a matrix such that AB’ and B’A are both defined, then order of matrix B is
(a) m × m
(b) n × n
(c) n × m
(d) m × n

Answer

Answer: (d) m × n

Question 45.
If A and B are matrices of same order, then (AB’ – BA’) is a
(a) skew symmetric matrix
(b) null matrix
(c) symmetric matrix
(d) unit matrix

Answer

Answer: (a) skew symmetric matrix

Question 46.
If A is a square matrix such that A² = I, then (A – I)³ + (A + I)³ – 7A is equal to
(a) A
(b) I – A
(c) I + A
(d) 3 A

Answer

Answer: (a) A

Question 47.
For any two matrices A and B, we have
(a) AB = BA
(b) AB ≠ BA
(c) AB = 0
(d) None of these

Answer

Answer: (d) None of these

Question 48.
If A = [a_ij]_2×2 where a_ij = i + j, then A is equal to
(a) \(\left[\begin{array}{cc}
1 & 2 \\
3 & 4
\end{array}\right]\)
(b) \(\left[\begin{array}{cc}
2 & 3 \\
3 & 4
\end{array}\right]\)
(c) \(\left[\begin{array}{cc}
1 & 1 \\
2 & 2
\end{array}\right]\)
(d) \(\left[\begin{array}{cc}
1 & 2 \\
1 & 2
\end{array}\right]\)

Answer

Answer: (b) \(\left[\begin{array}{cc}
2 & 3 \\
3 & 4
\end{array}\right]\)

Question 49.
The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is
(a) 18
(b) 512
(c) 81
(d) None of these

Answer

Answer: (b) 512

Question 50.
The order of the single matrix obtained from
\(\left[\begin{array}{cc}
1 & -1 \\
0 & 2 \\
2 & 3
\end{array}\right]\) \(\left\{\left[\begin{array}{ccc}
-1 & 0 & 2 \\
2 & 0 & 1
\end{array}\right]-\left[\begin{array}{ccc}
0 & 1 & 23 \\
1 & 0 & 21
\end{array}\right]\right\}\) is
(a) 2 × 2
(b) 2 × 3
(c) 3 × 2
(d) 3 × 3

Answer

Answer: (d) 3 × 3

Question 51.
A square matrix A = [a_ij]_n×n is called a diagonal matrix if a_ij = 0 for
(a) i = j
(b) i < j
(c) i > j
(d) i ≠ j

Answer

Answer: (d) i ≠ j

Question 52.
A square matrix A = [a_ij]_n×n is called a lower triangular matrix if a_ij = 0 for
(a) i = j
(b) i < j
(c) i > j
(d) None of these

Answer

Answer: (b) i < j

Question 53.
The matrix A = \(\left[\begin{array}{cc}
0 & 1 \\
1 & 0
\end{array}\right]\) is a
(a) unit matrix
(b) diagonal matrix
(c) symmetric matrix
(d) skew symmetric matrix

Answer

Answer: (c) symmetric matrix

Question 54.
If \(\left[\begin{array}{cc}
x+y & 2x+z\\
x-y & 2z+2
\end{array}\right]\) = \(\left[\begin{array}{cc}
4 & 7 \\
0 & 10
\end{array}\right]\) then find the value of x, y, z and w respectively
(a) 2, 2, 3, 4
(b) 2, 3, 1, 2
(c) 3, 3, 0, 1
(d) None of these

Answer

Answer: (a) 2, 2, 3, 4

Question 55.
If \(\left[\begin{array}{cc}
x-y & 2x+z\\
2x-y & 3z+w
\end{array}\right]\) = \(\left[\begin{array}{cc}
-1 & 5 \\
0 & 13
\end{array}\right]\) then the value of w is
(a) 1
(b) 2
(c) 3
(d) 4

Answer

Answer: (d) 4

Question 56.
Find x, y, z and w respectively such that
\(\left[\begin{array}{cc}
x-y & 2x+z\\
2x-y & 2x+w
\end{array}\right]\) = \(\left[\begin{array}{cc}
5 & 3 \\
12 & 15
\end{array}\right]\)
(a) 7, 2, 1, 1
(b) 7, 5, 3, 8
(c) 1, 2, 5, 6
(d) 6, 3, 2, 1

Answer

Answer: (a) 7, 2, 1, 1

Question 57.
If \(\left[\begin{array}{cc}
a+b & 2\\
5 & ab
\end{array}\right]\) = \(\left[\begin{array}{cc}
6 & 2 \\
5 & 8
\end{array}\right]\) then find the value of a and b respectively
(a) 2, 4
(b) 4, 2
(c) Both (a) and (b)
(d) None of these

Answer

Answer: (c) Both (a) and (b)

Question 58.
For what values of x and y are the following matrices equal
A = \(\left[\begin{array}{cc}
2x+1 & 3y\\
0 & y^{2}-5y
\end{array}\right]\) B = \(\left[\begin{array}{cc}
x+3 & y^{2}+2 \\
0 & -6
\end{array}\right]\)
(a) 2, 3
(b) 3, 4
(c) 2, 2
(d) 3, 3

Answer

Answer: (c) 2, 2

Question 59.
If A = \(\left[\begin{array}{cc}
α & 0\\
1 & 1
\end{array}\right]\) and B = \(\left[\begin{array}{cc}
1 & 0 \\
5 & 1
\end{array}\right]\) then find value of α for which A² = B is
(a) 1
(b) -1
(c) 4
(d) None of these

Answer

Answer: (d) None of these

Question 60.
If P = \(\left[\begin{array}{ccc}
i & 0 & -i \\
0 & -i & i \\
-i & i & 0
\end{array}\right]\) and Q = \(\left[\begin{array}{cc}
-i & i \\
0 & 0 \\
i & -i
\end{array}\right]\) then PQ is equal to
(a) \(\left[\begin{array}{cc}
-2 & 2 \\
1 & -1 \\
1 & -1
\end{array}\right]\)
(b) \(\left[\begin{array}{cc}
2 & -2 \\
-1 & 1 \\
-1 & 1
\end{array}\right]\)
(c) \(\left[\begin{array}{cc}
2 & -2\\
-1 & 1
\end{array}\right]\)
(d) \(\left[\begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array}\right]\)

Answer

Answer: (b) \(\left[\begin{array}{cc}
2 & -2 \\
-1 & 1 \\
-1 & 1
\end{array}\right]\)

Question 61.
\(\left[\begin{array}{c}
1 & x & 1
\end{array}\right]\) \(\left[\begin{array}{ccc}
1 & 3 & 2 \\
2 & 5 & 1 \\
15 & 3 & 2
\end{array}\right]\) \(\left[\begin{array}{c}
1 \\
2 \\
x
\end{array}\right]\)
(a) -7
(b) -11
(c) -2
(d) 14

Answer

Answer: (c) -2

Question 62.
If A = \(\left[\begin{array}{cc}
1 & -1\\
2 & -1
\end{array}\right]\) B = \(\left[\begin{array}{cc}
x & 1\\
y & -1
\end{array}\right]\) and (A + B)² = A² + B², then x + y is
(a) 2
(b) 3
(c) 4
(d) 5

Answer

Answer: (d) 5

Question 63.
If AB = A and BA = B, then
(a) B = 1
(b)A = I
(c) A² = A
(d) B² = I

Answer

Answer: (c) A² = A

Question 64.
If A = \(\left[\begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
a & b & -1
\end{array}\right]\) then (A – I) (A + I) = 0 for
(a) a = b = 0 only
(b) a = 0 only
(c) b = 0 only
(d) any a and b

Answer

Answer: (d) any a and b

Question 65.
If A = \(\left[\begin{array}{cc}
1 & 1\\
0 & 2
\end{array}\right]\) then A⁸ – 2⁸ (A – I)
(a) I – A
(b) 2I – A
(c) I + A
(d) A – 2I

Answer

Answer: (b) 2I – A

Question 66.
If A = \(\left[\begin{array}{ccc}
2 & 2 & 1 \\
1 & 3 & 1 \\
1 & 2 & 2
\end{array}\right]\) then A³ – 7A² + 10A =
(a) 5I + A
(b) 5I – A
(c) 5I
(d) 6I

Answer

Answer: (b) 5I – A

Question 67.
If A is a m × n matrix such that AB and BA are both defined, then B is an
(a) m × n matrix
(b) n × m matrix
(c) n × n matrix
(d) m × m matrix

Answer

Answer: (b) n × m matrix

Question 68.
If A = \(\left[\begin{array}{cc}
1 & 2\\
3 & 4
\end{array}\right]\) then A² – 5A is equal to
(a) 2I
(b) 3I
(c) -2I
(d) null matrix

Answer

Answer: (a) 2I

Question 69.
If A = \(\left[\begin{array}{cc}
-2 & 4\\
-1 & 2
\end{array}\right]\) then A² is
(a) null matrix
(b) unit matrix
(c) \(\left[\begin{array}{cc}
0 & 0\\
0 & 0
\end{array}\right]\)
(d) \(\left[\begin{array}{cc}
0 & 0\\
0 & 1
\end{array}\right]\)

Answer

Answer: (a) null matrix

Question 70.
If A and B are 2 × 2 matrices, then which of the following is true?
(a) (A + B)² = A² + B² + 2AB
(b) (A – B)² = A² + B² – 2AB
(c) (A – B)(A + B) = A² + AB – BA – B²
(d) (A + B) (A – B) = A² – B²

Answer

Answer: (c) (A – B)(A + B) = A² + AB – BA – B²

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