Maths · Algebra · chapter 3 of 13

Class 12 Maths Chapter 3: Matrices MCQs with answers

10 multiple-choice questions on Matrices, each with its answer and the reason, written from the NCERT chapter. For the CBSE board and JEE Main, which are set from the same NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter.

Question 1
For A = [[3, −1, 0, 5], [2, 7, −4, 1], [6, 8, 9, −2]], the value of a23 − a32 is
Show answer

Answer: (a) −12

a23 is in row 2, column 3: −4. a32 is in row 3, column 2: 8. So a23 − a32 = −4 − 8 = −12.

Question 2
A matrix has 12 elements and more rows than columns. The number of different orders it can have is
Show answer

Answer: (d) 3

An m × n matrix has mn elements, so mn = 12 with m > n. The pairs are 12 × 1, 6 × 2 and 4 × 3, so there are 3 orders.

Question 3
A = [aij] is a 2 × 3 matrix with aij = ij − 2. The sum of the elements in the second row of A is
Show answer

Answer: (d) 6

a21 = 2 − 2 = 0, a22 = 4 − 2 = 2, a23 = 6 − 2 = 4, so A = [[−1, 0, 1], [0, 2, 4]] and the second row sums to 0 + 2 + 4 = 6.

Question 4
Which of the following statements is true?
Show answer

Answer: (d) Every identity matrix is a scalar matrix.

An identity matrix is a diagonal matrix whose diagonal elements are all equal to 1, so it is a scalar matrix with k = 1. A scalar matrix with k = 3 is not an identity matrix; diag(1, 2) is diagonal but not scalar; [0, 0] is a zero matrix of order 1 × 2, not square.

Question 5
The matrix [[2x − 1, y − 3], [0, 5]] is a scalar matrix. Then x + y equals
Show answer

Answer: (a) 6

A scalar matrix is diagonal, so y − 3 = 0, y = 3; its diagonal elements are equal, so 2x − 1 = 5, x = 3. Hence x + y = 6.

Question 6
If [[x + y, 3], [2, x − y]] = [[9, 3], [2, 1]], then xy equals
Show answer

Answer: (c) 20

Equal matrices have equal corresponding elements: x + y = 9 and x − y = 1, so x = 5, y = 4 and xy = 20.

Question 7
A and C are matrices of order 2 × 3 and B is of order 3 × 2. Which of the following is defined?
Show answer

Answer: (d) A + C

A sum is defined only for matrices of the same order. A + C: both 2 × 3, defined. A + B: 2 × 3 and 3 × 2, not defined. AB is 2 × 2, so AB + C is not defined. BA is 3 × 3, so BA + C is not defined.

Question 8
If A = [[1, 0], [−2, 4]] and B = [[2, −3], [1, 5]], the element in the second row and first column of 3A − 2B is
Show answer

Answer: (a) −8

The (2, 1) element of 3A − 2B is 3a21 − 2b21 = 3(−2) − 2(1) = −8.

Question 9
If A = [[2, −1, 3], [0, 4, 1]] and B = [[1, 2], [5, −3], [−2, 0]], the element in the second row and first column of AB is
Show answer

Answer: (c) 18

The (2, 1) element of AB takes row 2 of A and column 1 of B: (0)(1) + (4)(5) + (1)(−2) = 0 + 20 − 2 = 18.

Question 10
A is a matrix of order 3 × 4. If both AB and BA are defined, the order of B is
Show answer

Answer: (c) order 4 × 3

For A of order m × n and B of order k × l, AB and BA are both defined if and only if n = k and l = m. Here m = 3, n = 4, so B is 4 × 3.

Take the free Class 12 Maths testSee the Class 12 flashcards

← Chapter 2: Inverse Trigonometric FunctionsChapter 4: Determinants →