If $\left[\matrix{\alpha & \beta \cr \gamma & -\alpha}\right]$ is to be square root of the two rowed unit matrix, then $\alpha, \beta$ and $\gamma$ should satisfy

Let $A = \left[\matrix{\alpha & \beta \cr \gamma & -\alpha}\right]$ $A^2 = I$ Multiply: $A^2 = \left[\matrix{\alpha^2 + \beta\gamma & 0 \cr 0 & \alpha^2 + \beta\gamma}\right]$ Equating with identity: $\alpha^2 + \beta\gamma = 1$ $\Rightarrow 1 - \alpha^2 - \beta\gamma = 0$ Final Answer: $\boxed{1 - \alpha^2 - \beta\gamma = 0}$