Let \(B=\left[\begin{matrix}1 & 3 \\ 1 & 5\end{matrix}\right]\) and A be a \(2\times 2\) matrix such that \(A{B}^{-1}={A…

Let \(B=\left[\begin{matrix}1 & 3 \\ 1 & 5\end{matrix}\right]\) and A be a \(2\times 2\) matrix such that \(A{B}^{-1}={A}^{-1}\). If \(BC{B}^{-1}=A\) and \({C}^{4}+\alpha {C}^{2}+\beta I=O\), then \(2\beta -\alpha\) is equal to

[JEE Main 2024, 9 Apr (Shift 2)]