Let α β ≠ 0 and A= [β, α, 3; α, α, β; -β, α, 2 α].If B= [3 α, -9, 3 α; -α, 7, -2 α; -2 α, 5, -2 β] is the matrix of cofactors of the elements of A,…

Let $\displaystyle \alpha \beta \neq 0$ and $\displaystyle A=\left[\begin{array}{rrr}\beta & \alpha & 3 \\ \alpha & \alpha & \beta \\ -\beta & \alpha & 2 \alpha\end{array}\right]$.If $\displaystyle B=\left[\begin{array}{rrr}3 \alpha & -9 & 3 \alpha \\ -\alpha & 7 & -2 \alpha \\ -2 \alpha & 5 & -2 \beta\end{array}\right]$ is the matrix of cofactors of the elements of $\displaystyle A$, then $\displaystyle \operatorname{det}(A B)$ is equal to :