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Suppose A is a 4 4 matrix. (a) Prove that every eigenvector of A is an eigenvector of A^2 3A + 2I (b)Suppose that the

Suppose A is a 4 4 matrix.

(a) Prove that every eigenvector of A is an eigenvector of A^2 3A + 2I

(b)Suppose that the eigenvalues of A are 2, 0, 1, and 2. What are the eigenvalues of A^2 3A+2I?

Please explain with detail.

Thanks!

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