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3_15

題目​

Find a matrix B≠I∈M2R\bm{B}\neq\bm{I}\in\mathcal{M}_2{\mathbb{R}} such that B3=I\bm{B}^3=\bm{I}

解答​

Choose B\bm{B} as follows, and it's easy to check.

[−1−110]\begin{bmatrix} -1 & -1\\ 1 & 0 \\ \end{bmatrix}