To raise a square (n × n) matrix A to a positive integer power n, one calculates An as A...

To raise a square (n × n) matrix A to a positive integer power n, one calculates Aⁿ as A · A · · · A (n times).

(a) Calculate successive powers A, A², A³, A⁴ of the

(b) Conjecture the general form of Aⁿ for the matrix A of part (a), where n is any positive integer.

(c) Prove your conjecture in part (b) using mathematical induction.