In: Advanced Math
Let A be a diagonalizable n × n matrix and let P be an invertible n × n matrix such that B = P−1AP is the diagonal form of A. Prove that Ak = PBkP−1, where k is a positive integer. Use the result above to find the indicated power of A. A = 6 0 −4 7 −1 −4 6 0 −4 , A5 A5 =