I think the problem that I was given by my school is wrong because
$ \forall v \in N(T)$ , $ Tv=0$ , so we have $ STv=S(0)=0$ . Thus, $ v \in N(T)$ implies $ v \in N(ST)$ . Hence, $ N(T) \subseteq N(ST)$ . Am I right?
Here, $ N(T), N(ST)$ means null space.
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