An integer matrix $M = \begin{bmatrix} -a& b& -c\\ d& e& f\\ g& h& -i \end{bmatrix}$ has determinant $c e g + b f g - c d h + a f h + b d i + a e i$.
Assume $0<a,b,c,d,e,f,g,h<B$ holds.
If you pick such an uniformly random matrix what is the probability that it is singular?