I want to list the elements of $\displaystyle T=<a,b : a^6=1, b^2=a^3,bab^{-1}=a^{-1} > $

So from my understanding, $\displaystyle a^ia^j=a^{i+j} \ \ \ \forall 0 \leq i,j \leq 5$ with $\displaystyle a^{i+j}=a^{i+j-6} \ \ i+j \geq 6 $

But I'm having trouble trying to make senses of the two other conditions, and how to properly translate them into the table.

Thank you!!!