A) \[1-{{\alpha }^{2}}+\beta \gamma =0\]
B) \[{{\alpha }^{2}}+\beta \gamma -1=0\]
C) \[1+{{\alpha }^{2}}+\beta \gamma =0\]
D) \[1-{{\alpha }^{2}}-\beta \gamma =0\]
Correct Answer: B
Solution :
We have\[\left[ \begin{matrix} \alpha & \beta \\ \gamma & -\alpha \\ \end{matrix} \right]\,\left[ \begin{matrix} \alpha & \beta \\ \gamma & -\alpha \\ \end{matrix} \right]=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\] \[\Rightarrow \] \[\left[ \begin{matrix} {{\alpha }^{2}}+\beta \gamma & 0 \\ 0 & {{\alpha }^{2}}+\beta \gamma \\ \end{matrix} \right]=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\] \[\Rightarrow \] \[{{\alpha }^{2}}+\beta \gamma -1=0\]
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