In a previous problem I asked about the notation used here.. I'm still not sure how to show it even though I now get what it's asking.
The following is an exercise from The Four Pillars of Geometry.
3.6.5. Show that the reflections in lines $L$, $M$, and $N$ (in that order) have the same outcome as reflections in lines $L'$, $M'$, and $N$, where $M'$ is perpendicular to $N$
I've had to ask around to clairify parts of the problem; it should be noted that the lines $L'$ and $M'$ are essentially arbitrary with no relation to $L$ and $M$ except that they appear in the same order when you do the reflections. Also, no picture is given as the lines are general though I've drawn a few pictures to help reason it out.
My main issue might be that I'm not sure what tools to use, so please be as specific as possible in your answer.