If \( A \) and \( B \) are symmetric matrices, then \( A B-B A \) is a \( \quad \) matrix. Select one: a. Skew symmetric b. Symmetric c. Column d. Diagonal

To determine the nature of the matrix \( C = AB - BA \) when \( A \) and \( B \) are symmetric, we can check whether \( C \) is symmetric or skew symmetric. A matrix \( C \) is skew symmetric if \( C^T = -C \). Calculating the transpose gives: \[ C^T = (AB - BA)^T = B^T A^T - A^T B^T = BA - AB = -C. \] Since \( C^T = -C \), it follows that \( C \) is skew symmetric. Therefore, the correct answer is: a. Skew symmetric