Matrices and Determinants: JEE Main 2023 Mathematics question

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 __________.