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.
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