Question

If A and B are symmetric matrices of the same order such that \( AB + BA = X \) and \( AB - BA = Y \), then \( (XY)^T = \)

• A. \( XY \)
• B. \( X^TY^T \)
• C. \( -YX \)
• D. \( -Y^TX^T \)

Hint:

Remember that \( (AB)^T = B^TA^T \), and if A is symmetric, \( A^T = A \).