Proof that f is a monomorphism

Question

let $f:A \rightarrow B$ and $g:B \rightarrow A$

given that $\;\;g \circ f = 1_A$

how can I prove that f is a monomorphism?

(I'm used to prove monomorphism in a different way, so I'm kind of lost)

Answer 1

Hint: Note that $$ f \circ \alpha = f \circ \beta \implies g \circ f \circ \alpha = g \circ f \circ \beta $$