3. Suppose that the characteristic polynomial of a square matrix A is fA(^) = –X³ + 3A (a) What is the size of A? (b) What are the eigenvalues of A? (c) What is tr(A)? (d) Is A invertible? Why or why not? Is A diagonalizable? If so, determine a diagonal matrix that is similar to A. (e) If not, explain why not.

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