JEE Mathematics Matrices MCQs Set B

Question. Statement -1 : If a matrix of order 2 × 2, commutes with every matrix of order 2 × 2, then it is scalar matrix.
Statement-2 : A scalar matrix of order 2 × 2 commutes with every 2 × 2 matrix.
(a) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
(b) Statement -1 is False, Statement-2 is True
(c) Statement -1 is True, Statement-2 is False.
(d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: A

Question. Statement 1 : If A and B are two matrices such that AB = B, BA = A then A² + B² = A + B
Statement 2 : A and B are idempotent matrices.
(a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
(c) Statement -1 is False, Statement-2 is True.
(d) Statement -1 is True, Statement-2 is False.

Answer: A

Question. If a square matrix A is such that AA^T = I = A^T A, then | A | is equal to :
(a) ± 1
(b) 0
(c) ± 2
(d) none

Answer: A

Question. If A is a skew symmetric matrix of order n and C is a column matrix of order n × 1, then C^T AC is:
(a) a zero matrix of order 1
(b) none of these
(c) an identity matrix of order 1
(d) an identity matrix of order n

Answer: A

Question. If A is a matrix of the order 3 and | A | = 8, then | adj A | is equal to
(a) 8²
(b) 8³
(c) 8
(d) 1

Answer: A

Question. Statement 1 : (a₁₁, a₂₂, .........a_nn) is a diagonal matrix then A^–1 = dia (a₁₁^–1, a₂₂^–1, a_nn^–1)
Statement 2 : If A = dia (2, 1, –3) and B = dia (1, 1, 2) then det (AB^–1) = 3
(a) Statement -1 is True, Statement-2 is False.
(b) Statement -1 is False, Statement-2 is True.
(c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
(d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: A