theorem Th51: :: MATRIX_9:51

for n being Nat
for K being Field
for M being Matrix of n,K st ex i being Element of NAT st
( i in Seg n & ( for k being Element of NAT st k in Seg n holds
(Col (M,i)) . k = 0. K ) ) holds
the addF of K $$ ((In ((Permutations n),(Fin (Permutations n)))),(Path_product M)) = 0. K