The norm of a polynomial f in a skew polynomial ring must be in the center

Question

This is proved in Prop 1.7.1 in Jacobson's book ``Finite dimensional division algebras over fields". But I am not clear why the norm n(f), defined as the norm of the matrix representation of f by right multiplication on the K[$x^m$] left module K[x,$\sigma$], must be in $F(x^m)$, with F=invariant subfield of $\sigma$ in $K$ and $m$=order of $\sigma$. Can anyone give some hint? Thanks!