Negative of Product Inverse

Theorem
Let $\left({R, +, \circ}\right)$ be a ring with unity.

Let $z \in U_R$, where $U_R$ is the set of units.

Then:
 * $\left({- z}\right)^{-1} = - \left({z^{-1}}\right)$.

where $z^{-1}$ is the ring product inverse of $z$.

Proof
Let the unity of $\left({R, +, \circ}\right)$ be $1_R$.

Thus:
 * $\left({- z}\right)^{-1} = - \left({z^{-1}}\right)$