A) \[-\frac{1}{13}\left[ \begin{matrix} 1 & 7 \\ 8 & 3 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} -1 & 8 \\ 2 & -3 \\ \end{matrix} \right]\]
C) \[-\frac{1}{13}\left[ \begin{matrix} 1 & -8 \\ -2 & 3 \\ \end{matrix} \right]\]
D) does not exist
Correct Answer: B
Solution :
\[A=\left[ \begin{matrix} 3 & 8 \\ 2 & 1 \\ \end{matrix} \right]\] \[|A|=\left| \begin{matrix} 3 & 8 \\ 2 & 1 \\ \end{matrix} \right|=3-16=-13\] \[adj(A)={{\left[ \begin{matrix} 1 & -2 \\ -8 & 3 \\ \end{matrix} \right]}^{T}}=\left[ \begin{matrix} 1 & -8 \\ -2 & 3 \\ \end{matrix} \right]\] \[\therefore \] \[{{A}^{-1}}=\frac{adj(A)}{|A|}=-\frac{1}{13}\left[ \begin{matrix} 1 & -8 \\ -2 & 3 \\ \end{matrix} \right]\]
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