# Definition:Opposite Magma

## Definition

Let $\left({S, \circ}\right)$ and $\left({S, *}\right)$ be magmas.

Then $\left({S, *}\right)$ is the **opposite magma of $\left({S, \circ}\right)$** if and only if:

- $\forall x, y, z \in S: x \circ y = z \iff y * x = z$

The operation $*$ is sometimes referred to as the **opposite law** of $\circ$.

## Also known as

This concept was introduced with this name in the books by Nicolas Bourbaki.

Other sources refer to $\left({S, *}\right)$, as defined here, as the **($1$-$2$) parastrophe of $\left({S, \circ}\right)$**.