If \( A=\operatorname{diag}\left(\begin{array}{lll}a & b & c\end{ar...

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If \( A=\operatorname{diag}\left(\begin{array}{lll}a & b & c\end{array}\right) \), show that \( A^{n}=\operatorname{diag}\left(a^{n} b^{n} \quad c^{n}\right) \) for all positive integer \( n \).
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