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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: A

Solution

The product (I - A) [cos α -sin α; sin α cos α] simplifies to I + A because the matrix A represents a rotation transformation, and when combined with the identity matrix I, it results in an additive effect that incorporates both the identity and the rotation.

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