Let A = (a) By calculating and factorizing CA(x), 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= ju v and B= o (c) Using the fact that 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 Br