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For the matrix function F(α)=[cosα, -sinα, 0; sinα, cosα, 0; 0, 0, 1], where α is a real number, which of the following equals [F(α)]⁻¹?

1. F(−α)
2. F(α⁻¹)
3. F(2α)
4. None of these

Correct answer: F(−α)

Solution

F(alpha) is a rotation through angle alpha about the z-axis, so its inverse is the rotation through -alpha, i.e. [F(alpha)]^-1 = F(-alpha).

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