A) \[\left[ \begin{matrix} 1 & -2 \\ -3 & 5 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} -1 & 2 \\ 3 & -5 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} -1 & -2 \\ -3 & -5 \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} 1 & 2 \\ 3 & 5 \\ \end{matrix} \right]\]
Correct Answer: B
Solution :
Let \[A=\left[ \begin{matrix} 5 & 2 \\ 3 & 1 \\ \end{matrix} \right];|A|=-1,\] Cofactors of \[A,C=\left[ \begin{matrix} 1 & -3 \\ -2 & 5 \\ \end{matrix} \right]\] \[\Rightarrow \] adj \[(A)=C'=\left[ \begin{matrix} 1 & -2 \\ -3 & 5 \\ \end{matrix} \right]\] \[\therefore \] \[{{A}^{-1}}=\frac{1}{|A|}adj\,(A)\] \[=\frac{1}{-1}\left[ \begin{matrix} 1 & -2 \\ 3 & -5 \\ \end{matrix} \right]\] \[=\left[ \begin{matrix} -1 & 2 \\ 3 & -5 \\ \end{matrix} \right]\]
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