Let Λ be an associative ring with 1 and let b{cyrillic} be a net of ideals in Λ of order n. A net subgroup G(b{cyrillic}) in the general linear group GL(n,Λ) is defined to be the largest subgroup in the multiplicative system e+M(b{cyrillic}), where M (b{cyrillic}) is a subring in the ring of matrices M(n,Λ) associated with b{cyrillic} and e is the unit matrix. This implies that an invertible matrix x, is contained in G(b{cyrillic}) if and only if both the matrices x and x^-1 are contained in e+M(b{cyrillic}). The question arises: for which rings is the second of these conditions a consequence of the first?