Introduction to groups

Suppose $X$ is a two-element set and $Y$is a three-element set. Are $S(X)$ and $S(Y)$ abelian groups?

(Recall that for $S(X)$ to be abelian, the compositions $f \circ g$ and $g \circ f$ must coincide as mappings for any bijections $f$ and $g$ from $X$ to $X$.

If $$f(g(x)) \neq g(f(x))$$ for some $x$, the group of bijections is non-abelian.)