OK, $\displaystyle t_{ab}=ax+b$. I have to prove this is a subgroup of S4. Now, Ive already proved closure by composition $\displaystyle t_{ab}=ax+b$ with $\displaystyle t_{cd}=cx+d$ to yield $\displaystyle (ac)x+(ad+b)$.

Now, the identities wrt composition are $\displaystyle a=1$ and $\displaystyle b=0$. What is the inverse!? How would you find the inverse wrt composition here?

Thanks!