Let B= [1, 3; 1, 5] and A be a 2 × 2 matrix such that A B^-1=A^-1. If B C B^-1=A and C^4+α C^2+β I=O, then 2 β-α is equal to

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