Question

Show that the composition is a reflection.​

Answer 1

Answer:

Consider a 2×2 matrix that reflects about a line through the origin that makes an angle θ with the x-axis:

Lθ=[cos(2θ)sin(2θ)sin(2θ)−cos(2θ)]

This can also be thought of as the composition of three matrices. First a rotation matrix by −θ, then a reflection about the x-axis, then a rotation by θ back.