C2 x C2 Abelian

It's something you can prove.

Say your group is $\{ e,a,b,ab \}$. We want to find the value of $ba$. By closure of the group, we must have $ba = e,a,b$ or $ab$. If $ba=e$ then $a = ea = baa = ba^2=be=b$, which isn't true since $a \ne b$, so $ba \ne e$. You can show that $ba \ne a$ and $ba \ne b$ in similar ways.

Alternatively, you can show that $ba = (ab)^{-1}$ and use the fact that the non-identity elements have order 2 to deduce that $ba=ab$.