1. The problem statement, all variables and given/known data Let L denote the line through the origin in R2 that that makes angle -∏ < theta ≤ ∏ with the positive x-axis. The reflection operator that reflects points about L in R2 is the matrix transformation R2 --> R2 with standard matrix [cos 2(theta) sin 2(theta); sin 2(theta) -cos 2(theta)] Show that the composition of a rotation operator followed by a re reflection operator is another reflection operator. 2. Relevant equations Standard matrix for reflection in R2 comes to mind; [cos(theta) -sin(theta); sin (theta) cos (theta)] These are 2x2 matrices and I'm not sure how to input them here so I put ; to seperate the two columns. 3. The attempt at a solution I'm kind of confused as to how to attempt to solve the question. I mean I could use the 2 standard matrices and use matrix multiplication which gives a really ugly 2x2 that I'm not sure what to do with. Any help to get me started would be appreciated :).