Let $l=P+[v]$ be a line. Let $m=Q+[v]$. Show that if $|v|=1$, then $Ω_{l}Ω_{m}=τ_{w}$, where $w=2<P-Q,V^{⟂}>V^{⟂}$ and $Ω_{m}Ω_{l}=τ_{-w}$
I honestly have no idea how to start this. I know the following definitions:
For a line $l$, the reflection in $l$ is the mapping $Ω_{l}x=x-2<x-p,N>N$ where $N$ is a unit normal to $l$ and $P$ is any point of $l$.
If $v=(v_{1}, v_{2})$, then $V^{⟂}=(-v_{2}, v_{1})$
We haven't covered product of reflections nor translations so I don't know the definitions. Literally any help is appreciated. Thanks for your time.