Extended Real Numbers under Multiplication form Commutative Monoid

Theorem
Denote with $\overline{\R}$ the extended real numbers.

Denote with $\cdot_{\overline{\R}}$ the extended real multiplication.

The algebraic structure $\left({\overline{\R}, \cdot_{\overline{\R}}}\right)$ is a commutative monoid.

Proof
By Extended Real Numbers form Monoid under Multiplication, $\left({\overline{\R}, \cdot_{\overline{\R}}}\right)$ is a monoid.

By Extended Real Multiplication is Commutative, $\cdot_{\overline{\R}}$ is commutative.

Hence $\left({\overline{\R}, \cdot_{\overline{\R}}}\right)$ is a commutative monoid.