Show that R is nonsingular and R^-1 (inverse) = R^T (transpose) [Linear Algebra]

R = [cosθ -sinθ
sinθ cosθ]

(This is the rotation matrix which rotates a vector by an angle θ counter clockwise.)

det(R) = cos^2 θ + sin^2 θ = 1 ==> R is nonsingular.

R^-1 = [cosθ sinθ | -sinθ cosθ]

R^t = [cosθ sinθ | -sinθ cosθ]

==> R^-1 = R^t