If \( A=\left[\begin{array}{lll}3 & 2 & 0 \\ 1 & 4 & 0 \\ 0 & 0 & 5...

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If \( A=\left[\begin{array}{lll}3 & 2 & 0 \\ 1 & 4 & 0 \\ 0 & 0 & 5\end{array}\right] \), show that \( A^{2}-7 A+10 I_{3}=O \).
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