Question 69

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

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