Let A = (a) By calculating and factorizing CA(2), the characteristic polynomial of A, show that -1 is the only eigenvalue of A, and then find a corre- sponding eigenvector u. (b) Find a vector v E R2 such that (A + I)v = u, and show by direct calculation that P-1AP = B where P = [u v and B= (c) Using the fact that B" = (-1)" for every integer n, find A" explicitly in terms of n. Hint: Begin by using the equality A = PBP- to express A" in terms of P and B"