Matrices And Determinants

Let A be a symmetric matrix such that \(\mathrm{|A|=2}\) and \(\left[ {\matrix{ 2 & 1 \cr 3 & {{3 \over 2}} \cr } } \right]A = \left[ {\matrix{ 1 & 2 \cr \alpha & \beta \cr } } \right]\). If the sum of the diagonal elements of A is \(s\), then \(\frac{\beta s}{\alpha^2}\) is equal to __________.