Properties of Norm on Division Ring/Norm of Negative

Theorem
Let $\struct {R, +, \circ}$ be a division ring with unity $1_R$.

Let $\norm {\,\cdot\,}$ be a norm on $R$.

Let $x \in R$.

Then:
 * $\norm {-x} = \norm x$

Proof
By Norm of Negative of Unity:
 * $\norm {-1_R} = 1$

Then:

as desired.