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.
Matrices Class 12 MCQs Questions with Answers
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 = [aij]m×n is said to be symmetric if
(a) aij = 0
(b) aij = aji
(c) aij = aij
(d) aij = 1
Answer
Answer: (b) aij = aji
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 = [aij]m×n is said to be skew symmetric if
(a) aij = 0
(b) aij = aji
(c) aij = -aji
(d) aij = 1
Answer
Answer: (b) aij = aji
Matrices MCQ Class 12 Chapter 3 Question 7.
A = [aij]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 + AT = 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 = [aij]2×2 where aij = {\(_{0 if i = j}^{1 if i ≠ j}\) 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 = [aij]2×2 where aij = 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 = [aij]n×n is called a diagonal matrix if aij = 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 = [aij]n×n is called a lower triangular matrix if aij = 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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