(xy)^(-1) = b^(-1)a^(-1),
keeping in mind the group may not be commutative. Thanks.
Say that $\displaystyle x^{-1} = y$. What does that mean? It means that $\displaystyle xy = e$ and $\displaystyle yx=e$. That is the definition of what it means to be a multiplicative inverse. In your problem you have $\displaystyle x=ab$ and $\displaystyle y=b^{-1}a^{-1}$.