 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2021/paper-1/5/d/ii/solution

Both factors and their product are real, so the Hermitian conjugate equals the transpose. Part (i) therefore gives

R_{1}^{†} R_{1} = R_{1}^{T} R_{1} = I .

Hence

R_{1} is unitary for every θ, ϕ .

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