# MCQ Questions for Class 12 Maths Chapter 3 Matrices with Answers

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## Matrices Class 12 MCQs Questions with Answers

Don’t forget to practice the multitude of MCQ Questions on Matrices Class 12 with answers so you can apply your skills during the exam.

Question 1.
If A = [aij]m × n is a square matrix, if:
(a) m < n
(b) m > n
(c) m = n
(d) None of these.

Question 2.
Which of the given values of x and y make the following pair of matrices equal:
$$\left[\begin{array}{cc} 3 x+7 & 5 \\ y+1 & 2-3 x \end{array}\right]$$ $$\left[\begin{array}{lc} 0 & y-2 \\ 8 & 4 \end{array}\right]$$
(a) x = –$$\frac { 1 }{3}$$, y = 7
(b) Not possible to find
(c) y = 7, x = –$$\frac { 2 }{3}$$
(d) x = –$$\frac { 1 }{3}$$, y = –$$\frac { 2 }{3}$$

Answer: (b) Not possible to find

Question 3.
The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is
(a) 27
(b) 18
(c) 81
(d) 512.

Assume X, Y, Z, W and P are matrices of order 2 × n, 3 × 1, 2 × p, n × 3 and p × k respectively. Now answer the following (4-5):
Question 4.
The restrictions on n, k and p so that PY + WY will be defined are
(a) k = 3, p = n
(b) k is arbitrary, p = 2
(c) p is arbitrary
(d) k = 2,p = 3.

Answer: (a) k = 3, p = n

Question 5.
If n =p, then the order of the matrix 7X – 5Z is:
(a) p × 2
(b) 2 × n
(c) n × 3
(d) p × n.

Question 6.
If A, B are symmetric matrices of same order, then AB – BA is a
(a) Skew-symmetric matrix
(b) Symmetric matrix
(c) Zero matrix
(d) Identity matrix.

Question 7.
If A = $$\left[\begin{array}{l} \cos \alpha-\sin \alpha \\ \sin \alpha \cos \alpha \end{array}\right]$$ then A + A’ = I, the value of α is
(a) $$\frac { π }{6}$$
(b) $$\frac { π }{3}$$
(c) π
(d) $$\frac { 3π }{2}$$

Answer: (a) $$\frac { π }{6}$$

Question 8.
Matrices A and B will be inverse of each other only if:
(a) AB = BA
(b) AB – BA = O
(c) AB = O, BA = I
(d) AB = BA = I.

Answer: (d) AB = BA = I.

Question 9.
If A = $$\left[\begin{array}{lr} \alpha & \beta \\ \gamma & -\alpha \end{array}\right]$$ is such that A² = I, then
(a) 1 + α² + ßγ = 0
(b) 1 – α² + ßγ = 0
(c) 1 – α² – ßγ = 0
(d) 1 + α² – ßγ = 0

Answer: (c) 1 – α² – ßγ = 0

Question 10.
If a matrix is both symmetric and skew- symmetric matrix, then:
(a) A is a diagonal matrix
(b) A is a zero matrix
(c) A is a square matrix
(d) None of these.

Answer: (b) A is a zero matrix

Question 11.
If A is a square matrix such that A² = A, then (I + A)³ – 7A is equal to :
(a) A
(b) I – A
(c) I
(d) 3A.

Question 12.
The matrix A = $$\left[\begin{array}{lll} 0 & 0 & 5 \\ 0 & 5 & 0 \\ 5 & 0 & 0 \end{array}\right]$$ is a
(a) scalar matrix
(b) diagonal matrix
(c) unit matrix
(d) square matrix.

Question 13.
If matrix A = [aij]2×2
where aij = 1 if i ≠ j = 0 if i = j,
(a) I
(b) A
(c) O
(d) None of these

Question 14.

then A – B is equal to
(a) I
(b) O
(c) 2I

Question 15.
If A is a 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.

Question 16.
For any two matrices A and B, we have :
(a) AB = BA
(b) AB ≠ BA
(c) AB = 0
(d) None of these.

Question 17.
The number of 3 × 3 non-singular matrices, with four entries as 1 and all other entries as 0, is:
(a) less than 4
(b) 5
(c) 6
(d) at least 7.

Hint:
First row with exactly one zero total number of cases = 6.
First row with 2 zeroes, we get more cases.
∴ Total no. of non-singular matrices = 7.

Question 18.
If A is an 3 × 3 non-singular matrix such that AA’ = A’A and B = A-1 A’, then BB’ equals
(a) I
(b) B-1
(c) (B-1)’
(d) I + B.

B = A-1A’
⇒ AB = A’
ABB’ = A’B’
⇒ ABB’ = (BA)’ = (A-1 A’A)’
= (A-1 AA’)’ = (A’)’ = A
BB’ = I.

Fill in the Blanks

Question 1.
If $$\left[\begin{array}{ll} 1 & 2 \\ 2 & 1 \end{array}\right]$$ $$\left[\begin{array}{l} x \\ y \end{array}\right]$$ = $$\left[\begin{array}{l} 5 \\ 4 \end{array}\right]$$ then value of y is ………………..

Question 2.
If A is an m × n matrix such that AB and BA are defind, then B is of order …………….

Question 3.
A diagonal matrices is said to be ……………… if its diagonal elements are equal (other than unity).

Question 4.
For a 2 × 2 matrix, A = [aij], whose elements are given by aij = $$\frac { i }{j}$$, then a12 = ………………..

Answer: $$\frac {1}{2}$$

Question 5.
If $$\left[\begin{array}{cc} a-b & 2 a+c \\ 2 a-b & 3 c+d \end{array}\right]$$ = $$\left[\begin{array}{cc} -1 & 5 \\ 0 & 13 \end{array}\right]$$

Question 6.
If A is a square matrix of order m, and if there exists another square matrix B of the same order m, such that AB = BA = I, then B is called the ……………….

Question 7.
If A is of order m × n and B is also of order m × n, then (A + B) is a matrix of order ………………..

Question 8.
If [5 x 1] $$\left[\begin{array}{l} 4 \\ 2 \\ 7 \end{array}\right]$$ = 35 then x = ………………

Question 9.
For any matrix A, A – A’ is …………….. matrix.

If A = $$\left[\begin{array}{cc} 2 & -2 \\ -2 & 2 \end{array}\right]$$ and A² = λA, then λ = ………………..