Show that all positive integral powers of a symmetric matrix aresymmet – InterviewSolution

1.	Show that all positive integral powers of a symmetric matrix aresymmetric.
Answer» Let `A` is a symmetric matrix, then, we have to prove, `(A^n)^T = A^n` We know, `(AB)^T = B^TA^T` `:. (A^n)^T = (AA...A)^T = A^TA^T*A^T...A^T = (A^T)^n = A^n` `=> (A^n)^T = A^n`. It shows all positive integral powers of a symmetric matrix are symmetric.

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