definition of unimodular group Suppose $G$ is a locally compact group,we call $G$ an unimodular group if the modular function $\Delta =1$,that is to say,if the left Haar measure is also a right Haar measure. How to show that "$\Delta =1$ if and only if the left Haar measure is also a right Haar measure.

By definition of the modular function, if $\
u$ is a right Haar measure, then for every $g\in G$, we have $\
u(g^{-1}S)=\Delta(g)\
u(S)$ for all open $S\subseteq G$.
Now if $\Delta \equiv 1$, then $\
u$ becomes left invariant, too, since $\
u(g^{-1}S)=\
u(S)$.
The converse follow similarly.