7. If A is a square matrix, remember that the characteristic polynomial of A is det (A – AI) and that the roots of the characteristic polynomial are the eigenvalues of A. a. Explain why A and AT have the same characteristic polynomial. b. Explain why A and A" have the same set of eigenvalues. c. Suppose that A is diagonalizable with diagonalization A = PDP-1. Explain why AT is diagonalizable and find a diagonlization.

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