How Might I Show That Aut(Z) Has Order 2?

[PennState666]

Homework Statement

prove Aut(Z) has order 2.

Homework Equations

none

The Attempt at a Solution

The generators for Z = <-1, 1>.
if f is a mapping in Aut(Z), f(x)= x or f(x) = -x

 

[Dick]

Sure, the two elements of Aut(Z) are f(x)=x, and f(x)=(-x). Any question?

 

[PennState666]

how might I show that Aut(Z) has order 2?

 

[Dick]

how might I show that Aut(Z) has order 2?

You just did. Doesn't that show that there are two elements in Aut(Z)? A generator must map to a generator if you are going to get an automorphism.