Don't understand this reasoning with respect to linear operators.(adsbygoogle = window.adsbygoogle || []).push({});

Let S and T be linear operators on the finite dimensional vector space V. Then assuming the composition ST is invertible, we get

[tex]\text{null} \; S \subset \text{null} \; ST [/tex]

Why is that? I thought hard about it but I simply cannot follow. Is it not possible to have an element x of V that is in the nullspace of S but not in the nullspace of ST ? i.e. S maps x to 0 but T maps x to y where S don't map y to 0 ?

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# Don't understand this simple vector space problem

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