A) \[\frac{1}{10}\left[ \begin{matrix} 1 & -2 \\ 3 & 4 \\ \end{matrix} \right]\]
B) \[\frac{1}{10}\left[ \begin{matrix} 4 & 2 \\ -3 & 1 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} 4 & 2 \\ -3 & 1 \\ \end{matrix} \right]\]
D) \[\frac{1}{10}\left[ \begin{matrix} 4 & -2 \\ -3 & 1 \\ \end{matrix} \right]\]
Correct Answer: B
Solution :
We know \[{{A}^{-1}}\frac{ad\,j\,A}{\left| A \right|}\] \[\therefore \] \[adjA=\left[ \begin{matrix} 4 & 2 \\ -3 & 1 \\ \end{matrix} \right]\] \[\left| A \right|=\left| \begin{matrix} 1 & -2 \\ 3 & 4 \\ \end{matrix} \right|\] \[=4+6=10\] \[\therefore \] \[{{A}^{-1}}=\frac{ddj\,A}{\left| A \right|}=\frac{1}{10}\left[ \begin{matrix} 4 & 2 \\ -3 & 1 \\ \end{matrix} \right]\]
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