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A square matrix X is periodic if Xn = I, the identity matrix, and its period is n.
If n = 1 then trivially, X = I, and Xk = I for all k.
However, if n > 1, then Xn = I but Xk is not I for any k < n.
Then Xna+b = Xna*Xb = Ia*Xb = Xb for all a. That is, X has a period of n.
It can be shown that X, X2, ... , Xn-1 and I are distinct matrices that form a Group
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