A) \[\left[ \begin{matrix} 47 & -39/2 \\ -41 & 17 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} 94 & -82 \\ -39 & 34 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} -47 & 46 \\ 39/2 & -17 \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} -47 & 39/2 \\ 46 & -17 \\ \end{matrix} \right]\]
Correct Answer: A
Solution :
Given that, \[{{A}^{-1}}=\left[ \begin{matrix} 5 & -2 \\ -7 & 3 \\ \end{matrix} \right]\] and \[{{B}^{-1}}=\frac{1}{2}\left[ \begin{matrix} 9 & -7 \\ -8 & 6 \\ \end{matrix} \right]\] Now, we have \[{{(AB)}^{-1}}={{B}^{-1}}.{{A}^{-1}}\] \[=\frac{1}{2}\left[ \begin{matrix} 9 & -7 \\ -8 & 6 \\ \end{matrix} \right]\,\,\left[ \begin{matrix} 5 & -2 \\ -7 & 3 \\ \end{matrix} \right]\] \[=\frac{1}{2}\left[ \begin{matrix} 45+49 & -18-21 \\ -40-42 & 16+18 \\ \end{matrix} \right]\] \[=\frac{1}{2}\left[ \begin{matrix} 94 & -39 \\ -82 & 34 \\ \end{matrix} \right]=\left[ \begin{matrix} 47 & -39/2 \\ -41 & 17 \\ \end{matrix} \right]\]
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