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Anonymous User Best Answer
suppose A⁶=I, so that x⁶−1 annihilates A. Then m(x) is of degree at most 2, and m(x) divides x⁶−1. Hence m(x) is either x−1, x+1, (x−1)(x+1), x²−x+1, or x²+x+1. m(x) divides c(x), and m(x) and c(x) have the same roots, so c(x) must respectively be either (x−1)², (x+1)², (x−1)(x+1), x²−x+1, or x²+x+1. So total possiblty 5