Question

If A, B are symmetric matrices of same order, then AB − BA is a ______.

Options

• Skew symmetric matrix

• Symmetric matrix

• Zero matrix

• Identity matrix

Answer 1

If A, B are symmetric matrices of same order, then AB − BA is a skew symmetric matrix.

Explanation:

We know that A' = A, B' = B

So, (AB – BA)' = (AB)' – (BA)'

= B'A' – A'B' 

= BA – AB

= –(AB – BA)

AB – BA is a skew-symmetric matrix.