矩阵幂的痕迹

考虑\(2\)by \(2\)矩阵\[A = \begin{pmatrix} 5 & 1 \\ -1 & 3 \end{pmatrix}。\(A^{100}?\)

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注意:\(2\)-by-\(2\)矩阵的迹定义为\[\text{Tr}\begin{pmatrix} a & b \\ c& d\ end{pmatrix} = a+d\;\]。