Past exam of the mathematics course of the University of Oxford / 2021 / Prelims / Mathematics I / 5 / c / i / Solution

An injective function from a finite set to itself is surjective: its image of a function contains as many distinct elements as the entire set, so it cannot omit one. Thus every element of $I(X)$ is a bijection, and conversely every bijection is injective. HenceIt is a group under function composition by i.