Question

I cam across this sentence that I need help understanding: "Since G is abelian (communatative), (ab^-1)=ab^-1*ab^-1"

Answer 1

What dose being communative have to do with (ab^-1)=ab^-1*ab^-1"

Answer 2

I'm assuming ab is denoted the operation on two unique elements a and b and then taking the inverse after this operation:
\[(a*b)^{-1} \]

It this correct?

Answer 3

yes thats right

Answer 4

I know communtaivety is ab=ba, but what does that have to do with (ab^-1)=ab^-1*ab^-1"

Answer 5

(ab^-1)=ab^-1*ab^-1=a^2(b^-1)^2=a^2(b^2)^-1=ee^-1=e

Answer 6

that was the rest of it

Answer 7

Does the text of the book look like this (the parenthesis is throwing me off)
\[ (ab)^{-1} = ab^{-1}*ab^{-1} \]