A) \[\left[ \begin{matrix} 1 & 2 \\ -3/2 & 3 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} 2 & -3 \\ 4 & 6 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} -2 & 4 \\ -3 & 6 \\ \end{matrix} \right]\]
D) Does not exist
Correct Answer: D
Solution :
Given,\[A=\left[ \begin{matrix} 2 & 3 \\ 4 & 6 \\ \end{matrix} \right]\], we know that \[{{A}^{-1}}=\frac{adj.A}{|A|}\]. Therefore, \[|A|\,\,=\,\,[12-12]=0.\] Since \[|A|\] is zero, therefore inverse of A does not exist.
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