Q. 633.7( 3 Votes )

# 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 :

Let C = (AB’ – BA’)

C’ = (AB’ – BA’)’

⇒ C’ = (AB’)’ – (BA’)’

⇒ C’ = (B’)’A’ – (A’)’B’

⇒ C’ = BA’ – AB’

⇒ C’ = -C

∴ C is a skew-symmetric matrix.

Clearly Option (A) matches with our deduction.

∴ Option (A) is the correct.

Rate this question :

Which of the following statements are True or False

AA’ is always a symmetric matrix for any square matrix A.

Mathematics - ExemplarWhich of the following statements are True or False

AA’ is always a symmetric matrix for any square matrix A.

Mathematics - ExemplarFill in the blanks in each of the

Sum of two skew symmetric matrices is always _______ matrix.

Mathematics - ExemplarFill in the blanks in each of the

If A and B are symmetric matrices, then

(i) AB – BA is a _________.

(ii) BA – 2AB is a _________.

Mathematics - ExemplarFill in the blanks in each of the

If A is a skew symmetric matrix, then A^{2} is a _________.

If A, B are square matrices of same order and B is a skew-symmetric matrix, show that A’ BA is skew symmetric.

Mathematics - ExemplarFill in the blanks in each of the

If A is symmetric matrix, then B’AB is _______.

Mathematics - ExemplarFill in the blanks in each of the

If A and B are symmetric matrices of same order, then AB is symmetric if and only if ______.

Mathematics - ExemplarShow that all the diagonal elements of a skew-symmetric matrix are zero.

Mathematics - Board Papers