If \( A=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right], B=...

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If \( A=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right], B=\left[\begin{array}{rr}1 & 0 \\ 0 & -1\end{array}\right] \) and \( C=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right] \), then show that \( A^{2}=B^{2}=C^{2}=I_{2} \).
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