Why $(M/M \operatorname{rad} A) \operatorname{rad}A=0$? Let $A$ be a ring and $M$ a right $A$-module. Why we have $(M/M \operatorname{rad}A) \operatorname{rad}A=0$? Thank you very much.

**Hint:** You can replace $\mathrm{rad}(A)$ with any right ideal of $A$.