 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2019-resit/11/b/i/solution

Each displayed Pauli matrix has zero trace and determinant

- 1

. Direct multiplication gives

σ_{i}^{2} = I

, hence

det σ_{i} = - 1, tr σ_{i} = 0, σ_{i}^{2} = I, σ_{i}^{- 1} = σ_{i} (i = x, y, z) .

Their two eigenvalues are therefore

+ 1

and

- 1

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