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Register a new userThe group invertibility of matrices over Bezout domains
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Let $R$ be a Bezout domain, and let $A,B,Cin R^{ntimes n}$ 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 Bezout domain, {it Electronic J. Linear Algebra}, {bf 18}(2009), 600--612).
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