Question

If $A=\left[\begin{array}{cc}\alpha & \beta \\ \gamma & -\alpha \end{array}\right]$ is such that $A^2=I$, then

• A. $1+{\alpha }^2+\beta \gamma =0$
• B. $1-{\alpha }^2+\beta \gamma =0$
• C. $1-{\alpha }^2-\beta \gamma =0$
• D. $1+{\alpha }^2-\beta \gamma =0$

Answer 1

Answer: (C)

$\left[\begin{array}{cc}\alpha & \beta \\ \gamma & -\alpha \end{array}\right]\left[\begin{array}{cc}\alpha & \beta \\ \gamma & -\alpha \end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$