The group invertibility of matrices over Bézout domains

Liu, Dayong and Fang, Aixiang (2024) The group invertibility of matrices over Bézout domains. Miskolc Mathematical Notes, 25 (1). pp. 373-381. ISSN 1787-2413

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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).

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