Group under composition of functions Let $T(S)$ be the set of all functions on $S = \{\ 1,2,3 \}\ $. $T(S)$ is a group under composition of functions.
I am to prove that this is either true or not. I would like some help understanding exactly what the author means by "Group under composition of functions". And can you give me an example of a set of all functions on some other set?

As @Sammy Black pointed out: 
Identity element in our case is the identity map but
Inverse element property fails in this case. Take the function $f(1)=f(2)=f(3)=1$ then there's no function $g$ such that $fog=gof=identity~ map$
