Question: Let A be a symmetric matrix. (a) Show that An is symmetric for any nonnegative integer n. (b) Show that 2A2 - 3A + I

Let A be a symmetric matrix.
(a) Show that An is symmetric for any nonnegative integer n.
(b) Show that 2A2 - 3A + I is symmetric.
(c) Show that any matrix polynomial p(A) of A, cf. Exercise 1.2.35, is a symmetric matrix.

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