Answer to Question #196385 in Linear Algebra for Rebecca

Question #196385

Prove that if A is a square matrix then AA^T and A + A are symmetric

Expert's answer

Let A be a square matrix.

Consider

"(AA^T)^T = (A^T)^TA^T= AA^T"

Hence "AA^T" is symmetric

Also, consider

"(A+A^T)^T = A^T + (A^T)^T = A^T + A = A+A^T"

Hence "A+A^T" is symmetric.

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