Question

Let $A$ be a symmetric matrix such that $|A|=2$ and $\begin{bmatrix} 2 & 1 \\\[0.3em] 3 & \frac 32 \\\[0.3em] \end{bmatrix}𝐴−\begin{bmatrix} 1 & 2 \\\[0.3em] α & β \\\[0.3em] \end{bmatrix}$. If the sum of the diagonal elements of $A$ is $s$, then $\frac {βs}{α^2}$ is equal to ____ .

Answer 1

The answer is 5.