(a)Prove that an orthogonal 2 ( 2 matrix must have the form

Where

Is a unit vector.
(b)Using part (a), show that every orthogonal 2 ( 2 matrix is of the form

Where 0 ( ( ( 2 (.

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or cos θ sin θ -sin θ cos θ | cos θ sin θ or cos θ | -cos θ R2 R2