Matrices And Determinants

Let \(A\) be a \(2 \times 2\) 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 \(A^{-1}=\alpha A+\beta I\), where \(I\) is an identity matrix of order \(2 \times 2\), then \(\alpha+\beta\) equals _________.