Question

If $A=\begin{bmatrix}\alpha&\beta\\ \gamma&-\alpha\end{bmatrix}$ 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)

$\begin{bmatrix}\alpha&\beta\\ \gamma&-\alpha\end{bmatrix}\begin{bmatrix}\alpha&\beta\\ \gamma&-\alpha\end{bmatrix}= \begin{bmatrix}1&0\\ 0&1\end{bmatrix}$