Composition or two reflections
In Euclidean space I know that the composition of two reflections is a rotation if the two lines you wish to reflect in cross. I need to prove this. It is for credit so NO ANSWERS PLEASE, but some hints at how to get started would be very much appreciated. If I fix a choice of coordinates in R^2 does that mean I can assume the two lines cross at the origin, without loss of generality, and then pick a frame? Or by picking a specific frame am I only proving it for that frame? Basically, I understand what is going on, I just dont know how to rigorously prove it and show that in this case you will always get a rotation of 2*theta about the point where the two lines of reflection cross, where theta is the angle between the two lines.