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