Orthogonal Matrices - Examples with Solutions

SOLVED:(a) Prove that an orthogonal 2 ×2 matrix must have the form [ a -b b a ] or [ a b b -a ] where [ a b] is a unit vector. (b) Using part (a), show that every orthogonal 2 ×2 matrix is of the form [ cosθ -sinθ sinθ cosθ ] or [ cosθ sinθ sinθ -cosθ ] where 0 ≤θ<2 π(c) Show that every orthogonal 2 ×2 matrix corresponds to either a rotation or a reflection in ℝ^2 (d) Show t