  Let $R$ be a B\'ezout domain, and let $A,B,C\in R^{n\times n}$ 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
B\'ezout domain, {\it Electronic J. Linear Algebra}, {\bf 18}(2009), 600--612).
