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 then:
 * $\norm{-1_R} = 1$.

Then:

as desired.