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Let A = [0 -tan(α/2); tan(α/2) 0] and let I denote the 2 × 2 identity matrix. Then the product (I − A) [cos α −sin α; sin α cos α] equals

1. I + A
2. I − A
3. A − I
4. A

Correct answer: I + A

Solution

With A=[[0,-t],[t,0]], t=tan(α/2), and using cosα=(1-t²)/(1+t²), sinα=2t/(1+t²), direct multiplication of (I−A) by the rotation matrix gives [[1,-t],[t,1]] = I + A.

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