\(\text{ Let }A=\left[\begin{matrix}1 & 2 \\ -1 & 4\end{matrix}\right].\text{ If }{A}^{-1}=\alpha I+\beta A,\alpha ,\bet…

\(\text{ Let }A=\left[\begin{matrix}1 & 2 \\ -1 & 4\end{matrix}\right].\text{ If }{A}^{-1}=\alpha I+\beta A,\alpha ,\beta \in R\text{. I is a }2\times 2\text{ identify matrix, then }4(\alpha -\beta )\text{ is equal to : }\begin{matrix}\end{matrix}\)

[JEE Main 2021, 27 Jul (Shift 1)]