Have you gone over the rational canonical form of a matrix? Or the CayleyHamilton theorem? If you have, question 1 should be straightforward. The answer to part (a) is yes (use the rational canonical form). For (b), use the CayleyHamilton theorem. For (c), write D = S^{1} T S, where S is an invertible matrix and D is diagonal. What's D^{2}?
