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.