theorem Th53: :: MATRIX14:53

for n being Element of NAT
for K being Field
for A being Matrix of n,K st A <> 0. (K,n) holds
ex B, C being Matrix of n,K st
( B is invertible & C is invertible & ((B * A) * C) * (1,1) = 1. K & ( for i being Element of NAT st 1 < i & i <= n holds
((B * A) * C) * (i,1) = 0. K ) & ( for j being Element of NAT st 1 < j & j <= n holds
((B * A) * C) * (1,j) = 0. K ) )