If \( A=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & 0 \\ a & b & -1\end...

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If \( A=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & 0 \\ a & b & -1\end{array}\right] \) and \( I \) is the unit matrix of order 3 , then show that \( A^{2}+2 A^{4}+4 A^{6}=7 A^{8} \)
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