theorem Th38: :: MATRIX14:38

for n being Element of NAT
for K being Field
for a being Element of K
for P being Matrix of n,K st n > 0 & a <> 0. K & P * (1,1) = a " & ( for i being Element of NAT st 1 < i & i <= n holds
P . i = Base_FinSeq (K,n,i) ) holds
P is invertible