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Let f(α)=[cosα, sinα; -sinα, cosα]. If α, β, and γ are the angles of a triangle, then the product f(α)f(β)f(γ) is equal to

1. I₂
2. -I₂
3. 0
4. None of these

Correct answer: -I₂

Solution

Each matrix is a rotation by -a, so the product is a rotation by -(alpha+beta+gamma). In a triangle alpha+beta+gamma=pi, giving rotation by -pi, which is the matrix [[-1,0],[0,-1]] = -I_2.

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