# Negative of Ring Negative

## Theorem

Let $\struct {R, +, \circ}$ be a ring.

Let $a \in R$ and let $-a$ be the ring negative of $a$.

Then:

$-\paren {-a} = a$

## Proof

The ring negative is, by definition of a ring, the inverse element of $a$ in the additive group $\struct {R, +}$.

The result then follows from Inverse of Group Inverse.

$\blacksquare$