 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-2/12/b/iv/solution

Multiply

A^{2} = - I /4

A

once more:

A^{3} = - \frac{1}{4} A = (0 1/8 - 1/8 0) .

No additional diagonalization is needed.

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