If A and B are symmetric matrices, then AB - BA is
Answer & explanation
Correct answer: option 4
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