- #1
xsw001
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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