A) \[-\frac{1}{8}\left[ \begin{matrix} 3 & 1 \\ -2 & 2 \\ \end{matrix} \right]\]
B) \[-\frac{1}{8}\left[ \begin{matrix} -2 & -3 \\ -2 & 1 \\ \end{matrix} \right]\]
C) \[\frac{1}{8}\left[ \begin{matrix} -1 & -3 \\ -2 & 2 \\ \end{matrix} \right]\]
D) None of these
Correct Answer: B
Solution :
We have \[A=\left[ \begin{matrix} 1 & 3 \\ 2 & -2 \\ \end{matrix} \right]\] Then, adj \[A={{\left[ \begin{matrix} -2 & -2 \\ -3 & 1 \\ \end{matrix} \right]}^{T}}\] \[=\left[ \begin{matrix} -2 & -3 \\ -2 & 1 \\ \end{matrix} \right]\] and \[|A|=\left| \begin{matrix} 1 & 3 \\ 2 & -2 \\ \end{matrix} \right|\] \[=-2-6=-8\] \[\therefore \] \[{{A}^{-1}}=\frac{1}{\left| A \right|}(adj\,A)\] \[\Rightarrow \] \[{{A}^{-1}}=-\frac{1}{8}\left[ \begin{matrix} -2 & -3 \\ -2 & 1 \\ \end{matrix} \right]\]
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