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## Main Question or Discussion Point

If V is any vector space and S and T are linear operators on V such that ST=TS show that the null space and the range of T are invariant under S.

I think I need to begin by taking an element of the range of T and having S act on it and show that it stays in V? Can you help get me started?

I think I need to begin by taking an element of the range of T and having S act on it and show that it stays in V? Can you help get me started?