Proof that if $L \subset \mathfrak{sl}(V)$ then $L$ is semisimple

Question

I am trying to show that if $V$ is finite dimensional over $\mathbb{C}$, and we have a Lie algebra $L \subset \mathfrak{sl}(V)$ such that the natural representation $(V, \rho:L \subset \mathfrak{gl}(V) )$ is irreducible, then $L$ is semisimple.

Not really sure what to do. Any ideas?