JEE Mathematics Matrices MCQs Set 01

Question. The matrix [a₁x₁ + a₂x₂ + a₃x₃] is of order :
(a) 1 × 1
(b) 1 × 2
(c) 1 × 3
(d) 2 × 1

Answer: A

Question. The inverse of a symmetric matrix is
(a) a symmetric matrix
(b) square matrix
(c) skew symmetric matrix
(d) diagonal matrix

Answer: A

Question. If A = [a_ij] is a skew-symmetric matrix of order n, then a_ij is equal to:
(a) 0 for all i = 1, 2, ...n
(b) 1 for all i = 1, 2,..., n
(c) 0 for some i
(d) 1 for some i

Answer: A

Question. If | A | = 2 and A is a 2 × 2 matrix, then the value of det. {adj. {adj. (adj. A2)}} is equal to:
(a) 4
(b) 64
(c) 16
(d) 128

Answer: A

Question. If A is an invertible matrix and B is a matrix, then:
(a) rank (AB) = rank (B)
(b) rank (AB) > rank (A)
(c) rank (AB) = rank (A)
(d) rank (AB) > rank (B)

Answer: A

Question. If A and B are Hermition matrices of the same order, then (AB – BA) is:
(a) a Skew-Hermition matrix
(b) a null matrix
(c) a Hermition matrix
(d) none of these

Answer: A

Question. Let A and B be two matrices then (AB)' equals:
(a) B'A'
(b) – AB
(c) A'B
(d) 1

Answer: A

Question. If A is n × n matrix, then adj (adj A) =
(a) | A |^n–2 A
(b) | A |^n–1 A
(c)   none
(d) | A |ⁿ A

Answer: A