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