1.
Let α(0,)\alpha \in (0, \infty) and A=(12α101012)A = \begin{pmatrix} 1 & 2 & \alpha \\ 1 & 0 & 1 \\ 0 & 1 & 2 \end{pmatrix}. If det(adj(2AAT)adj(A2AT))=28\det\bigl(\text{adj}(2A - A^T) \cdot \text{adj}(A - 2A^T)\bigr) = 2^8, then (detA)2(\det A)^2 is equal to: