(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I was reading my text book and i encountered this....--->>

" For instance if f,g,h are in A(S) and fg = fh then g=h " I understand this part... because we can take the the inverse of f both sides and say g=h.

then it says--->> " If gf = f^(-1)g but since f ≠ f^(-1) we cannot cancel the g here"

SO MY QUESTION IS

IF gf = f^(-1)g then ....why can't we take inverse of g both sides and show f = f^(-1) and say f = f^(-1) and g = g.

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# Homework Help: The set of 1-1 Mapping of S Onto itself

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