# A basic question on group theory

Let, $$G$$ be a group and $$a,bin G$$. If $$a^{-1}b^2a=b^3$$ and $$b^{-1}a^2b=a^3$$ then show that $$a=b=e$$, where $$e$$ is the identity of $$G$$.

We have from the first condition, $$b^{27}=a^{-1}b^{18}a$$. Then what to do?

Any hint.?