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If $A=\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{array}\right]$ then $A^5=$
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$16 \mathrm{~A}$
$A=\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{array}\right]$ $\Rightarrow A^5=\left[\begin{array}{ccc}2^5 & 0 & 0 \\ 0 & 2^5 & 0 \\ 0 & 0 & 2^5\end{array}\right]=$ $=2^4\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{array}\right]$
$=16 \mathrm{~A}$
$=16 \mathrm{~A}$
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