# Product of Absolute Values of Integers

## Theorem

Let $a, b \in \Z$ be integers.

Let $\size a$ denote the absolute value of $a$:

$\size a = \begin {cases} a & : a \ge 0 \\ -a : a < 0 \end {cases}$

Then:

$\size a \times \size b = \size {a \times b}$

## Proof

From Integers form Ordered Integral Domain, $\Z$ is an ordered integral domain.

The result follows from Product of Absolute Values on Ordered Integral Domain.

$\blacksquare$