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Showing a set of subspaces are subspaces of a homomorphism?

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1 another question from a problem set that I am struggling to answer. Any guidance or help would be appreciated. I don't even really understand what the question is asking. Let $V$ be a nonzero vector space and let $T in text{Hom}(V, V )$. Show that ${S in Hom(V, V ) : S circ T = T circ S }$ is a subspace of $ text{Hom}(V, V )$. linear-algebra vector-spaces proof-writing dual-spaces share | cite | improve this question edited Jan 4 at 5:54 André 3000 12.5k 2 20 42 asked Jun 5 '17 at 11:55