Question

If A, B are Symmetric matrices of same order, then AB – BA is a

Options

• Skew symmetric matrices

• Symmetric matrix

• Zero matrix

• Identity matrix

Answer 1

Skew symmetric matrices

Explanation:

As A and B are symmetric matrices, we have A = A and B = B.

Here, (AB – BA) = (AB) – (BA)

= BA – AB

= – (AB – BA)

∴ (AB –BA) = – (AB – BA)

Hence (AB – BA) is a skew-symmetric matrix.