# noncommutative algebra – Prime rings and commuting ideals

Question : Show that
$$R$$ is a prime ring containing two commuting non-zero left ideals $$I$$ and $$J$$ $$implies R$$ is commutative.
Where “commuting ideals” means $$ij=ji$$ for all $$i in I$$, $$j in J$$
My attempt : Let $$x, y in R, quad xIyJ=yJxI$$ and I need a hint to accomplish the proof.