Question

If A and B are symmetric matrices of the same order, then AB – BA is ______.

Options

• Skew – symmetric matrix

• Symmetric matrix

• Diagonal matrix

• Identity matrix

Answer 1

If A and B are symmetric matrices of the same order, then AB – BA is skew – symmetric matrix.

Explanation:

Given that A and B are symmetric matrices,

A = A’ and B = B’

Then (AB – BA)’ = (AB)’ – (BA)’

= B’A’ – A’B’  ...[∵ A = A’, B = B’]

= BA – AB

= – (AB – BA)

Thus, it is skew – symmetric.