#### Question

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

#### Solution

It is given that *A* and *B* are symmetric matrices. Therefore, we have:

Thus, (*AB* − *BA*) is a skew-symmetric matrix.

Is there an error in this question or solution?

Solution If a and B Are Symmetric Matrices, Prove that Ab − Ba is a Skew Symmetric Matrix Concept: Symmetric and Skew Symmetric Matrices.