Let A be a 2 × 2 matrix with real entries such that A^′=α A + I, where α ∈ R -{-1,1}. If det (A^2-A)=4, then the sum of all possible values of α is…

Let A be a $\displaystyle 2 \times 2$ matrix with real entries such that $\displaystyle \mathrm{A}^{\prime}=\alpha \mathrm{A}+\mathrm{I}$, where $\displaystyle \alpha \in \mathbb{R}-\{-1,1\}$. If $\displaystyle \operatorname{det}\left(A^2-A\right)=4$, then the sum of all possible values of $\displaystyle \alpha$ is equal to