Prove that if in a group G, then .
My proof so far:
Now (ab)^{2}=a^{2}b^{2} for each a,b \in G,
so
implies
then, there exist a^{-1},b^{-1} in G
(a^-1)(a^2b^2)(b^-1) = (a^-1)(b^2a^2)(b^-1)
ab=ba.
Am I allow to switch the a and b like that?
Prove that if in a group G, then .
My proof so far:
Now (ab)^{2}=a^{2}b^{2} for each a,b \in G,
so
implies
then, there exist a^{-1},b^{-1} in G
(a^-1)(a^2b^2)(b^-1) = (a^-1)(b^2a^2)(b^-1)
ab=ba.
Am I allow to switch the a and b like that?