If $A=\begin{bmatrix}\alpha & \beta\\\gamma & -\alpha\end{bmatrix}$ is such that $A^2=I,$ then which of the following is true:

Question

$$\begin{array}{1 1}(A)\;1+{\alpha}^2+\beta\gamma =0& (B)\;1-{\alpha}^2+\beta\gamma=0\\(C)\;1-{\alpha}^2-\beta\gamma=0 & (D)\;1+{\alpha}^2-\beta\gamma=0\end{array}$$