Inversion of Matrices over a Commutative Semiring

@inproceedings{Reutenauer1984InversionOM,
  title={Inversion of Matrices over a Commutative Semiring},
  author={Christophe Reutenauer and Howard Straubing},
  year={1984}
}
It is a well-known consequence of the elementary theory of vector spaces that if A and B are n-by-n matrices over a field (or even a skew field) such that AB = 1, then BA = 1. This result remains true for matrices over a commutative ring, however, it is not, in general, true for matrices over noncommutatives rings. In this paper we show that if A and B are n-by-n matrices over a commutative semiring, then the equation AB = 1 implies BA = 1. We give two proofs: one algebraic in nature, the other… CONTINUE READING
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