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## Main Question or Discussion Point

G is a group. Let x be an element of G.

Prove x^2=1 if and only if the order of x is 1 or 2.

How do I approach this problem?

I know since G is a group, all the elements in there have the following four properties:

1) Closure: a, b in G => a*b in G

2) Associative: (a*b)*c=a*(b*c)

3) Unique identity (e) exists: a*e=e*a=a

4) Unique inverse exists: a*a^(-1)=a^(-1)*a=e

Prove x^2=1 if and only if the order of x is 1 or 2.

How do I approach this problem?

I know since G is a group, all the elements in there have the following four properties:

1) Closure: a, b in G => a*b in G

2) Associative: (a*b)*c=a*(b*c)

3) Unique identity (e) exists: a*e=e*a=a

4) Unique inverse exists: a*a^(-1)=a^(-1)*a=e