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Show that whenever ab = ba, you have ba^(-1) = a^(-1)b.
I don't know how to slove problem.
pls help me..
I don't know how to slove problem.
pls help me..
No. I mean make left, then, on the result of the left multiplication, make a right multiplication. Let's see what you get.you mean that I have to make left and right..
make left:
ba^(-1) = a^(-1)b => aba^(-1) = aa^(-1)b
make right:
ba^(-1) = a^(-1)b => ba^(-1)a = a^(-1)ba
then what??
You started off correctly but made a typo (bolded) in the second step. Else you would have got the correct answer.ab=ba
a^(-1).ab.a^(-1) = a^(-1).ba.a^(-1)
(a^(-1).a) b^(-1) = a^(-1).b(a.a^(-1))
e.b^(-1) = a^(-1).b.e
b^(-1) = a^(-1).b
is that right?? I hope that I made it...