Show that a one-one function $f: \{1, 2, 3\} \rightarrow \{1, 2, 3\}$ must be onto.

(N/A) Let $A = \{1, 2, 3\}$. The function $f: A \rightarrow A$ is given as one-one.
By the definition of a one-one function,distinct elements in the domain $A$ must map to distinct elements in the codomain $A$.
Since the domain $A$ has $3$ elements,their images $f(1), f(2),$ and $f(3)$ must be $3$ distinct elements of the codomain $A$.
Because the codomain $A$ also contains exactly $3$ elements,the set of images ${f(1), f(2), f(3)}$ must be equal to the entire codomain $A$.
Therefore,every element in the codomain has a pre-image in the domain,which satisfies the definition of an onto function.
Thus,$f$ must be onto.