A) \[\left[ \begin{matrix} i & 0 \\ 0 & i/2 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} -i & 0 \\ 0 & -2i \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} i & 0 \\ 0 & 2i \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} 0 & i \\ 2i & 0 \\ \end{matrix} \right]\]
Correct Answer: B
Solution :
For\[A=\left[ \begin{matrix} i & 0 \\ 0 & i/2 \\ \end{matrix} \right]\], \[adj\,(A)=\left[ \begin{matrix} i/2 & 0 \\ 0 & i \\ \end{matrix} \right]\] and\[|A|=-\frac{1}{2}\]. \[\therefore \] \[{{A}^{-1}}=\frac{1}{\Delta }(adj\,A)=\frac{1}{-1/2}\,\left[ \begin{matrix} i/2 & 0 \\ 0 & i \\ \end{matrix} \right]=\left[ \begin{matrix} -i & 0 \\ 0 & -2i \\ \end{matrix} \right]\].
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