Rational Numbers under Multiplication form Monoid

Theorem
The set of rational numbers under multiplication $\left({\Q, \times}\right)$ forms a monoid.

Proof
Taking the monoid axioms in turn:

S0: Closure
Rational Multiplication is Closed.

S1: Associativity
Rational Multiplication is Associative.

S2: Identity
Rational Multiplication Identity is $1$.

Hence the result.