1.
Let α,βR\alpha, \beta \in \mathbb{R} and let A=(βα3ααββα2α)A = \begin{pmatrix} \beta & \alpha & 3 \\ \alpha & \alpha & \beta \\ -\beta & \alpha & 2\alpha \end{pmatrix}. If B=(3α93αα72α2α528)B = \begin{pmatrix} 3\alpha & -9 & 3\alpha \\ -\alpha & 7 & 2\alpha \\ -2\alpha & 5 & -28 \end{pmatrix} is the matrix of cofactors of the elements of AA, then det(AB)\det(AB) is equal to: