The commuting inverses of a square matrix
M. J. Englefield · Mathematical Proceedings of the Cambridge Philosophical Society · 1966
An inverse AI for an arbitrary matrix A was first given by Moore (4). Since the application to solution of linear equations only depended on the property A AI A = A, Bjerhammar (2) used this equation to define the set of generalized inverses AI. If A is regular, then only the regular inverse A−1 satisfies this definition. If A is a generalized inverse of AI, so that AI = AI AAI, then AI is a reciprocal inverse.