question_answer 1)

If A and B are symmetric matrices, prove that AB – BA is a skew symmetric matrix. 

Answer:

Given A and B are symmetric matrices          A? = A               ? (1)             B? = B               ? (2)       Now (AB ? BA)? = (AB)? ? (BA)?       = B?A? ? A?B? [                         = BA ? AB [Using (1) and (2)]              is a skew symmetric matrix.