Question: (a) Prove that the linear transformation associated with the improper orthogonal matrix is a reflection through the line that makes an angle 1/2 Î¸ with

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

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

Cos sin sin -cos

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