prove that distinct reflections commute iff...

let $\displaystyle m$ and $\displaystyle l$ be lines in $\displaystyle E_2$, and the reflection of $\displaystyle l$ is the mapping $\displaystyle \Omega_l$ of $\displaystyle E_2$ to $\displaystyle E_2$ defined by $\displaystyle \Omega_lX = X - 2N((X - P) \cdot N)$ where $\displaystyle N$ is the unit normal to $\displaystyle l$ and $\displaystyle P$ is any point on $\displaystyle l$

Show that two distinct reflections $\displaystyle \Omega_l$ and $\displaystyle \Omega_m$commute if and only if $\displaystyle m \perp l$.