Let \(\alpha \beta \neq 0\) and \(A=\left[\begin{matrix}\beta & \alpha & 3 \\ \alpha & \alpha & \beta \\ -\beta & \alpha…

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

[JEE Main 2024, 5 Apr (Shift 2)]