A) \[\alpha \]
B) \[\beta \]
C) \[\gamma \]
D) None of these
Correct Answer: A
Solution :
[a] We have, \[\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]=\left[ \begin{matrix} \alpha & \beta \\ \gamma & \delta \\ \end{matrix} \right]\left[ \begin{matrix} \alpha & \beta \\ \gamma & \delta \\ \end{matrix} \right]\] \[=\left[ \begin{matrix} {{\alpha }^{2}}+\beta \gamma & \alpha \beta +\beta \delta \\ \alpha \gamma +\delta \gamma & \beta \gamma +{{\delta }^{2}} \\ \end{matrix} \right]\] \[\Rightarrow {{\alpha }^{2}}+\beta \gamma =1,\beta (\alpha +\delta )=0,\] \[\gamma (\alpha +\delta )=0,\beta \gamma +{{\delta }^{2}}=1\] \[\Rightarrow \beta =0=\gamma ,\alpha \ne -\delta \] and \[{{\alpha }^{2}}={{\delta }^{2}}\Rightarrow \delta =\alpha \]
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