8. Recall that a matrix A is symmetric if AT= A. (a) Prove that for every matrix A, the matrix A+A' is a symmetric matrix. (b) Prove that for cvcry n xn matriccs A, S, if S is symmctric, so is ASAT. (c) Prove for every n x n matrices A, P, B such that P is invertible and AP= PB. then det(A)=det(B). %3D

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