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

If A and 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: A) Skew-symmetric matrix

Explanation: For symmetric matrices A and B, A' = A and B' = B. Now (AB − BA)' = (AB)' − (BA)' = B'A' − A'B' = BA − AB = −(AB − BA). Thus AB − BA is skew-symmetric. Note: AB is symmetric only if A and B commute.