Question

If A, B are symmetric matrices of the same order then AB - BA is a

• A. Skew symmetric matrix
• B. Symmetric matrix
• C. Zero matrix
• D. Identity matrix.

Answer 1

Answer: (A)

Skew symmetric matrix

Answer 2

A and B are symmetric matrices $\Rightarrow \, A' = A$ $\Rightarrow \, B' = B$ Now $(AB - BA)' = (AB)' - (BA)'$ $= B'A' - A'B' = BA - AB$ $\because \, B' = B, A' = A = - (AB - BA)$ $\Rightarrow \, (AB - BA)$ is a skew symmetric matrix.