Abstract
In this paper, we study the recently defined notion of the inverse along an element. An existence criterion for the inverse along a product is given in a ring. As applications, we present the equivalent conditions for the existence and expressions of the inverse along a matrix.
Acknowledgements
The authors are highly grateful to the referee for valuable comments which led to improvements of the paper. In particular, Remarks 3.2 and 3.4 were suggested to the authors by the referee. The first author is grateful to China Scholarship Council for supporting him to purse his further study in University of Minho, Portugal.
Notes
No potential conflict of interest was reported by the authors.