Thursday, 25 February 2016

Please explain what's wrong with the proof that every group element is its own inverse.

What is wrong with my proof here?



Proof:



Let a,b be elements of a group and let aa=b.



Through manipulation, we see that
a=ba1


b1a=a1


b1aa1=e

b1=e



We of course know that
bb1=e
And from above, we see that
be=e
or
b=e.
And since aa=b, we can see that aa=e and that a=a1.

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