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

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


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) \(\frac{15}{2}\)


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

Answer

Answer: (a) I² = I


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


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


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


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


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’


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


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


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


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


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) \(\frac{1}{|A|}\)


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


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


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


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


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


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


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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