Question

If \(A\) is symmetric, \(P\) and \(B\) are skew symmetric matrices, then which of the following is correct?

• A. \(A^{13}B^{26} - B^{26}A^{13}\) is a symmetric matrix
• B. \(A^{26}P^{13} - P^{13}A^{26}\) is a skew symmetric matrix
• C. \(P^{13}A^{26} + A^{26}P^{13}\) is a skew symmetric matrix
• D. \(P^{13}B^{26} + B^{13}P^{26}\) is a skew symmetric matrix

Hint:

An odd power of a skew-symmetric matrix is skew-symmetric.
An even power of a skew-symmetric matrix becomes symmetric.
Any power of a symmetric matrix remains symmetric.

Answer 1

The Correct Option is C