Answer to Question #258108 in Statistics and Probability for Lira

Question

Let A be square matrix which of the following statements is correct?

A. A-A^T and (-A^TA^T) are symmetric

B. A+A^T is symmetric and (-A^TA^T) is skew symmetric

C.(-AA^T) is symmetric

D. A^TA and A+A^T are symmetric

Answer 1

by reversal law:

(-AA^T)^T= -((A^T)^TA^T) = -AA^T $\implies$ (A^T)^T = A

Therefore, -AA^T is symmetric.

Answer: C.(-AA^T) is symmetric