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Let $A$ be a unital noncommutative algebra and let $$0 \longrightarrow M_1 \longrightarrow M_2 \longrightarrow M_3 \longrightarrow 0$$ be a short exact sequence of $A$-bimodules. I think if the sequence splits as a sequence of left modules, then it has to split as a sequence of right modules. Someone knows if this is true or someone can give an explicit counterexample, please

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