Question

Let A be an abelian group. Show that if \[a \in A\] then \[-a \in A\]

Answer 1

Sorry. Show that \[-a \in A\] is unique.

Answer 2

abelian is a special kind of group right?
it has the commutative property i believe?

Answer 3

yeaps (:

Answer 4

groups have the inverse property
suppose a and b are in A
and a+b=0
b is the inverse of a

we want to show b=-a


a+b=0
(-a)+a+b=-a
0+b=-a
b=-a

is that what you want

Answer 5

i'm sleepy
i need to crash

Answer 6

i think so. thanks. (: