A) 5A
B) 10A
C) 16A
D) 32A
Correct Answer: C
Solution :
\[A=\left[ \begin{matrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \\ \end{matrix} \right]\,\Rightarrow {{A}^{5}}=\left[ \begin{matrix} {{2}^{5}} & 0 & 0 \\ 0 & {{2}^{5}} & 0 \\ 0 & 0 & {{2}^{5}} \\ \end{matrix} \right]={{2}^{4}}\left[ \begin{matrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \\ \end{matrix} \right]\] \[=16A\].
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