How to show that a non trivial exact functor is faithful.

Question

Let $F:\mathcal{A}\rightarrow \mathcal{B}$ be a non trivial functor between two abelian categories $\mathcal{A}$ and $\mathcal{B}$. Further, I know that $F$ is an exact functor. Now I want to show that $F$ is a faithful functor. For that I need to show that the map $Hom(X,Y)\rightarrow Hom(F(X),F(Y))$ is injective. I don't know how to prove that this map is injective. Is there any other way to prove that the functor $F$ is faithful.