Prove that, for any set $X$, $\mathrm{S}X$ is a group under function composition

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• Given a set $X$, a permutation of $X$ is a bijection $\sigma : X \longrightarrow X$. That is, it is a function with domain and codomain $X$ which is one to one and onto.

• Given a set $X$, the set $\mathrm{S}X$ is the set of all permutations of $X$.

Prove that, for any set $X$, $\mathrm{S}X$ is a group under function composition.

I understand the four properties it needs to prove that it's a group but I don't know how to apply it to this question.