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If $B = \begin{bmatrix} 5 & 2\alpha & 1 \ 0 & 2 & 1 \ \alpha & 3 & -1 \end{bmatrix}$ is the inverse of a $3 \times 3$ matrix $A$, then the sum of all values of $\alpha$ for which $\det(A) + 1 = 0$, is:
(1) $0$
(2) $-1$
(3) $1$
(4) $2$
BETA
