The group invertibility of matrices over Bézout domains

Dayong Liu; Aixiang Fang;


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

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