Mathematics Question from JEE Main 2023 · 29 January, Shift 2

Let $A$ be a symmetric matrix such that $|A| = 2$ and $\begin{bmatrix} 2 & 1 \\ 3 & \frac{3}{2} \end{bmatrix} A = \begin{bmatrix} 1 & 2 \\ \alpha & \beta \end{bmatrix}$. If the sum of the diagonal elements of $A$ is $s$, then $\dfrac{\beta s}{\alpha^2}$ is equal to: