I was working through presentation of the quaternion group (with element $8$), and I let $a = i$ and $b = j$. I immediately said $a^4 = b^4 = 1$, and $ab^2 a = 1$.
Since I have a relation for each generator and between the generator, I figured I have the whole presentation. However, when I looked up the presentation of the quaternion group, it was given as
$$Q=\langle F\{a,b\}\mid a^4=b^4=a^2b^2=1 , b^{-1} a d = a^{-1}\rangle.\tag{1}$$
It is hard for me to see whether my initial third relation is a mixture of 3rd or 4th relation given by $(1)$.
Also, when do I know if I have given enough relations? Do I have to just write it down and see?
Finding a presentation of a group seems quite tedious!