Let A be a 2 × 2 symmetric matrix such that A [1; 1] = [3; 7] and the determinant of A be 1. If A^-1=α A+β I, where I is an identity matrix of order…

Let $\displaystyle A$ be a $\displaystyle 2 \times 2$ symmetric matrix such that $\displaystyle A\left[\begin{array}{l}1 \\ 1\end{array}\right]=\left[\begin{array}{l}3 \\ 7\end{array}\right]$ and the determinant of $\displaystyle A$ be $\displaystyle 1$ . If $\displaystyle A^{-1}=\alpha A+\beta I$, where $\displaystyle I$ is an identity matrix of order $\displaystyle 2 \times 2$, then $\displaystyle \alpha+\beta$ equals $\displaystyle \_\_\_\_$