(a) Prove that the linear transformation associated with the improper orthogonal matrix

is a reflection through the line that makes an angle 1/2 θ with the x-axis.
(b) Show that the composition of two such reflections, with angles θ, φ, is a rotation. What is the angle of the rotation? Does the composition depend upon the order of the two reflections?

Transcribed Image Text:

Cos θ sin θ sin θ -cos θ