theorem Th35: :: MATRIX13:35

for n being Nat
for K being Field
for nt, nt1, nt2 being Element of n -tuples_on NAT
for M being Matrix of K
for perm being Element of Permutations n st nt1 = nt2 * perm holds
( Det (Segm (M,nt1,nt)) = - ((Det (Segm (M,nt2,nt))),perm) & Det (Segm (M,nt,nt1)) = - ((Det (Segm (M,nt,nt2))),perm) )