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 under Multiplication form Monoid, $\left({\overline \R, \cdot_{\overline \R}}\right)$ 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.