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For the matrix F(α) = [cos α −sin α 0; sin α cos α 0; 0 0 1], the product F(α)F(β) is equal to

1. F(αβ)
2. F(α/β)
3. F(α + β)
4. F(α - β)

Correct answer: F(α + β)

Solution

F(a) is a rotation by angle a (with a fixed third axis). The product of two rotations is rotation by the sum of the angles, so F(a)F(b) = F(a+b).

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