A) \[2\]
B) \[-2\]
C) \[\frac{1}{2}\]
D) \[-\frac{1}{2}\]
Correct Answer: D
Solution :
[d] We know that det \[(A)=\frac{1}{\det \,({{A}^{-1}})}\] \[{{A}^{-1}}\left[ \begin{matrix} 1 & -2 \\ -2 & 2 \\ \end{matrix} \right]\] \[\Rightarrow \,\left| {{A}^{-1}} \right|=\left| \begin{align} & \,\,1\,\,\,-2 \\ & -2\,\,\,\,\,2 \\ \end{align} \right|=2-4=-2\] \[\Rightarrow \det (A)=-\frac{1}{2}\]
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