Groups whose elements have order 2

[halvizo1031]

Homework Statement

suppose that G is a group in which every non-identity element has order two. show that G is commutative.

Homework Equations

The Attempt at a Solution

IS THIS CORRECT?

ab=a[(ab)^2]b=(a^2)(ba)(b^2)=ba

 

[lanedance]

yeah looks good (same as last post), if you want to include every step
ab = (ae)b = aeb = a (abab) b = (aa) ba (bb) = ebae = ba
does assume the multiplication is associative

 

[Dick]

Homework Statement

suppose that G is a group in which every non-identity element has order two. show that G is commutative.

Homework Equations

The Attempt at a Solution

IS THIS CORRECT?

ab=a[(ab)^2]b=(a^2)(ba)(b^2)=ba

Will you please stop posting the same question over and over again?