A) \[\frac{1}{ab-cd}\left[ \begin{matrix} b & -c \\ -d & a \\ \end{matrix} \right]\]
B) \[\frac{1}{ad-bc}\left[ \begin{matrix} b & -c \\ -d & a \\ \end{matrix} \right]\]
C) \[\frac{1}{ab-cd}\left[ \begin{matrix} b & d \\ c & a \\ \end{matrix} \right]\]
D) None of these
Correct Answer: A
Solution :
\[{{A}^{-1}}=\frac{adj\,A}{|A|}\] But \[|A|=\left| \,\begin{matrix} a & c \\ d & b \\ \end{matrix}\, \right|=ab-cd\] and \[adj\,A=\left[ \begin{matrix} b & -c \\ -d & a \\ \end{matrix} \right]\] therefore\[{{A}^{-1}}=\frac{1}{ab-cd}\left[ \begin{matrix} b & -c \\ -d & a \\ \end{matrix} \right]\].
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