Suppose a,b e G, where G is an abelian group under +. Show -(a + b) = (-a) + (-b).
Thanks for any help.
You need to keep in mind that if $\displaystyle \left(G,*\right)$ is a group $\displaystyle a,b\in G$, then $\displaystyle \left(a*b\right)^{-1}=b^{-1}*a^{-1}$. In additive notation, this would be the same as $\displaystyle -(a*b)=(-b)*(-a)$, where $\displaystyle *$ is a binary operation. In this case, that binary operation is $\displaystyle +$.
Does this clarify things?