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