Let $V$ be a vector space over a field $\mathbb{F}$ and let $L$, $M$ be two linear transformations from $V$ to itself.
a. Show that the subset $W= {x ∈ V : L(x) = M(x)}$ is a subspace of $V$
b. Suppose that $L\circ M = M\circ L$. Show that $L(E_{\lambda}(M))\subseteq E_{\lambda}(M)$ for all $\lambda\in F$.
I'm stuck on b but have included a in case it helps. At the moment i'm confused - I know $E_{\lambda}(M)$ is a subspace of $V$, and that $L(E_{\lambda}(M))=M(E_{\lambda}(L))$, but i'm not sure how this helps.