Counterexample to show the map $a \mapsto -a$ is not a binary operation

Question

The text in Dummit and Foote on pg-$16$ says:

$-$ (usual subtraction) is a non-commutative binary operation on $\mathbb{Z}$, where $-(a, b) = a-b$. The map $a \mapsto -a$ is not a binary operation (not binary).

I understand how subtraction is non-commutative. For example, $(-3)-(2)\neq (2)-(-3)$ How can I show by counterexample that the map $a \mapsto -a$ is not a binary operation?

Thanks.

Answer 1

A binary operation takes two inputs. The map $a\mapsto -a$ only takes one input.