A square matrix P satisfies \(P^2 = I - P\). If \(P^n = 5I - 8P\) then n is equal to
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Notice the sequence of coefficients of \(I\) and \(P\): \((0, 1) \rightarrow (1, -1) \rightarrow (-1, 2) \rightarrow (2, -3) \rightarrow (-3, 5) \rightarrow (5, -8)\). These are alternating signs of Fibonacci numbers!