Let A be a 2 × 2 matrix with real entries such that A'=α A+I, where α R-\-1,1. If det(A²-A)=4, then the sum of all possible values of α is equal to:

Matrices and Determinants: JEE Main 2023 Mathematics question

JEE Main 2023 · 11 Apr, Morning shift · Q4484

JEE Main 202311 Apr, Morning shiftMathematicsHardMatrices and Determinants245× since 2002

Let

\mathrm{A}

be a

2 \times 2

matrix with real entries such that

\mathrm{A}'=\alpha \mathrm{A}+\mathrm{I}

, where

\alpha \in \mathbb{R}-\{-1,1\}

. If

\operatorname{det}\left(A^{2}-A\right)=4

, then the sum of all possible values of

\alpha

is equal to :