A) \[\left[ \begin{matrix} -2 & 2 \\ 1 & -1 \\ 1 & -1 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} 2 & -2 \\ -1 & 1 \\ -1 & 1 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} 2 & -2 \\ -1 & 1 \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right]\]
E) \[\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\]
Correct Answer: B
Solution :
\[\therefore \]\[PQ=\left[ \begin{matrix} i & 0 & -i \\ 0 & -i & i \\ -i & i & 0 \\ \end{matrix} \right]\left[ \begin{matrix} -i & i \\ 0 & 0 \\ i & -i \\ \end{matrix} \right]\] \[=\left[ \begin{matrix} -{{i}^{2}}-{{i}^{2}} & {{i}^{2}}+{{i}^{2}} \\ 0+0+{{i}^{2}} & -{{i}^{2}} \\ {{i}^{2}} & -{{i}^{2}} \\ \end{matrix} \right]=\left[ \begin{matrix} 2 & -2 \\ -1 & 1 \\ -1 & 1 \\ \end{matrix} \right]\]
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