please explain #8

8. Let A be an n X n matrix. (a) Show that A and A have the same characteristic polynomial. (b) Explain why A and A have the same eigenvalues. (c) Show that if A is diagonalizable, then A" is diagonalizable. (d) Use your matrix from question 2 to give a 2 x 2 example where A and AT do not have the same eigenvectors