Abstract Algebra: Theory and Applications · Problem 1.10

Preliminaries — Thomas Judson

Mathematics — Abstract Algebra · functions-mappings

Problem

Let

f : A \to B

and

g : B \to A

be maps such that

g \circ f = \mathrm{id}_A

, where

\mathrm{id}_A

is the identity map on

A

. Prove that

f

is one-to-one and

g

is onto.