Suppose a,b e G, where G is an abelian group under +. Show -(a + b) = (-a) + (-b).

Thanks for any help.

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- Mar 9th 2009, 08:50 PMjzelltAbelian Group proof
Suppose a,b e G, where G is an abelian group under +. Show -(a + b) = (-a) + (-b).

Thanks for any help. - Mar 9th 2009, 09:10 PMChris L T521
- Mar 9th 2009, 09:14 PMjzellt
How do we know that -(a + b) = (-b) + (-a)?

Isn't that something I would have to show while giving a solid proof? - Mar 9th 2009, 09:17 PMChris L T521
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?