Subset Product/Examples/Subsets of Reals under Multiplication

Example of Subset Product
Let $\struct {\R, \times}$ be the multiplicative group of (non-zero) real numbers.

Let $S = \set {-1, 2}$.

Let $T = \set {1, 2, 3}$.

Then the subset product $S T$ is:
 * $ST = \set {-1, -2, -3, 2, 4, 6}$

Proof
Taking each ordered pair $\tuple {s, t}$ from $S \times T$: