Let $\alpha \in (0,\infty)$ and $A=\begin{bmatrix}1 & 2 & \alpha \\ 1 & 0 & 1 \\ 0 & 1 & 2\end{bmatrix}$. If $\det(\operatorname{adj}(2A-A^T)\cdot\operatorname{adj}(A-2A^T))=2^8$, then $(\det(A))^2$ is equal to: