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$$A = \begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1 \end{bmatrix}, B = \begin{bmatrix}0 & 0 & 1 \\0 & 1 & 0 \\1 & 0 & 0 \end{bmatrix} \Rightarrow A^{99} B^{100} + B^{99} A^{100} =$$
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