Let A = [α, 1, 2; 2, 3, 0; 0, 4, 5] and B = [1, 0, 0; 0, -5 α, 0; 0, 4 α, -2 α] + adj ( A ). If det ( B )=66, then det ( adj ( A )) equals:

Let $\displaystyle \mathrm{A}=\left[\begin{array}{lll}\alpha & 1 & 2 \\ 2 & 3 & 0 \\ 0 & 4 & 5\end{array}\right]$ and $\displaystyle \mathrm{B}=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & -5 \alpha & 0 \\ 0 & 4 \alpha & -2 \alpha\end{array}\right]+\operatorname{adj}(\mathrm{A})$. If $\displaystyle \operatorname{det}(\mathrm{B})=66$, then $\displaystyle \operatorname{det}(\operatorname{adj}(\mathrm{A}))$ equals :