MMN-4386
The group invertibility of matrices over Bézout domains
Dayong Liu;
Aixiang Fang;
Abstract
Let R be a Bézout domain, and let A,B,C ∈ Rn×n with ABA = ACA. If AB and CA are group invertible, we prove that AB is similar to CA. Moreover, we have (AB)# is similar to (CA)#. This generalize the main result of Cao and Li (Group inverses for matrices over a Bézout domain, Electronic J. Linear Algebra, 18 (2009), 600–612).
Vol. 25 (2024), No. 1, pp. 373-381