Answer to Question #118521 in Abstract Algebra for Jflows

Question

1.Let G be a group. Then left (ab right)^−1=______ for every A in G.
a.\\(b^{-1}a^{-1}\\)
b.\\(Ab\\)
c.\\(ba\\)
d.\\(A^{-1}b^{-1}\\)

Answer 1

$(ab)^{-1}ab=e$, so $(ab)^{-1}a=b^{-1}$ and $(ab)^{-1}=b^{-1}a^{-1}$

Answer: $(ab)^{-1}=b^{-1}a^{-1}$