Suppose $ f : S\_{n} \rightarrow (\mathbb{R} , + , 0 , - )$ is a group homomorphism. Prove $ f(S\_{n}) = {0} $, i.e., $f(\sigma) = 0$ for every $ \sigma \in S\_{n}$with $n \geq 1 $

I cannot seem to find the reason why the transpositions ( $ S\_{2} $ ) should have this property. This would of course immediately solve it. Help would be much appreciated!!