If B = [5, 2 α, 1; 0, 2, 1; α, 3, -1] is the inverse of a 3 × 3 matrix A, then the sum of all values of α for which det ( A )+1=0, is:

If $\displaystyle \mathrm{B}=\left[\begin{array}{ccc}5 & 2 \alpha & 1 \\ 0 & 2 & 1 \\ \alpha & 3 & -1\end{array}\right]$ is the inverse of a $\displaystyle 3 \times 3$ matrix A, then the sum of all values of $\displaystyle \alpha$ for which $\displaystyle \operatorname{det}(\mathrm{A})+1=0$, is :