A) \[\frac{1}{11}\left[ \begin{matrix} 1 & 2 \\ -3 & 5 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} 1 & 2 \\ -3 & 5 \\ \end{matrix} \right]\]
C) \[\frac{1}{13}\left[ \begin{matrix} -2 & 5 \\ 1 & 3 \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} 1 & 3 \\ -2 & 5 \\ \end{matrix} \right]\]
Correct Answer: A
Solution :
Let \[A=\left[ \begin{matrix} 5 & -2 \\ 3 & 1 \\ \end{matrix} \right]\] \[|A|=5+6=11\] and adj. \[A=\left[ \begin{matrix} 1 & 2 \\ -3 & 5 \\ \end{matrix} \right]\] \[{{A}^{-1}}=\frac{1}{|A|}\] (adj. A) \[=\frac{1}{11}\left[ \begin{matrix} 1 & 2 \\ -3 & 5 \\ \end{matrix} \right]\]
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