A) \[-\frac{1}{2}\left[ \begin{matrix} 4 & -2 \\ -3 & 1 \\ \end{matrix} \right]\]
B) \[\frac{1}{2}\left[ \begin{matrix} 4 & -2 \\ -3 & 1 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} -2 & 4 \\ 1 & 3 \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} 2 & 4 \\ 1 & 3 \\ \end{matrix} \right]\]
Correct Answer: A
Solution :
Given, \[A=\left[ \begin{matrix} 1 & 2 \\ 3 & 4 \\ \end{matrix} \right]\] Now, \[|A|=4-6=-2\] \[adj\,(A)=\left[ \begin{matrix} 4 & -2 \\ -3 & 1 \\ \end{matrix} \right]\] \[\therefore \] \[{{A}^{-1}}=\frac{adj\,(A)}{|A|}=-\frac{1}{2}\left[ \begin{matrix} 4 & -2 \\ -3 & 1 \\ \end{matrix} \right]\]
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