A) \[\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} 1 & 1 \\ 0 & 0 \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} -2 & 0 \\ 0 & -2 \\ \end{matrix} \right]\]
Correct Answer: A
Solution :
\[A.(adj\,(A)=|A|\,I\] Here\[|A|\,={{\cos }^{2}}x+{{\sin }^{2}}x=1\]. Hence, \[A.(adj\,(A))\,=\,\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\].
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