∀ {n : Type u_1} [inst : Fintype n] [inst_1 : DecidableEq n] {S : Type u_2} [inst_2 : CommRing S]
  [inst_3 : LinearOrder S] [IsStrictOrderedRing S] {A : Matrix n n S},
  (Pairwise fun i j => A i j < 0) → (∀ (j : n), 0 < ∑ i, A i j) → A.det ≠ 0