While learning about graphs, I came across theorem that I don't quite understand, and can't find a proof.
If G is bipartite, and $\det(A) \neq 0,$ then G has a perfect matching. (Given that matrix representation of G is A)
Ps.: I found bits of information, that proof may be connected with Edmonds Theorem, which I cannot find, since Edmonds-Karp Algorithm is way more popular in google ;)