If A and B are symmetric matrices, then AB - BA is

Skew symmetric matrix

The correct answer is Option (4) → Skew symmetric matrix

Given: A and B are symmetric matrices ⇒ $A' = A,\; B' = B$

Consider $(AB - BA)' = B'A' - A'B' = BA - AB = -(AB - BA)$

Hence, $(AB - BA)' = -(AB - BA)$

Therefore, $AB - BA$ is a skew-symmetric matrix.

Answer: Skew symmetric matrix