A) \[\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} 1 & 1 \\ 0 & 0 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} 0 & 0 \\ 1 & 1 \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \\ \end{matrix} \right]\]
Correct Answer: A
Solution :
We have \[A=\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \\ \end{matrix} \right]\] So \[{{A}^{2}}=\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \\ \end{matrix} \right]\,\,\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \\ \end{matrix} \right]=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]={{I}_{2}}\] \ \[{{A}^{4}}={{A}^{2}}.{{A}^{2}}={{I}_{2}}.{{I}_{2}}={{I}_{2}}=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\].
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