im given that $\displaystyle V$ and $\displaystyle W$ are vectors spaces now i need to show that the linear transformation $\displaystyle L(V,W)$ is a vector space.

Do I have to show the properties of a vector space.

Commutativy. i.e show $\displaystyle (S+T)=(T+S)$, such that $\displaystyle S,T \in L(V,W)$ and for an arbritary $\displaystyle v \in V$

I need some help here please