Let \(A\) be a \(2 \times 2\) matrix with real entries such that \(A^{\prime}=\alpha A+I\), where \(\alpha \in R -\{-1,1…

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

[JEE Main 2023, 11 Apr (Shift 1)]