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

A is said to be symmetric if    A^T = A

A is said to be skew-symmetric if    A^T = -A

 (AB - BA)^T    = (AB)^T - (BA)^T

                         = B^T A^T–A^T B^T

                         = BA - AB     since A and B are symmetric.

                         =- (AB - BA)