 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2017-resit/10/a/ii/2/solution

A^{*} = A

. Choose

A = (1 - i i 2), det A = 1.

Its off-diagonal entries are complex conjugates and its diagonal entries are real, so the defining condition holds. It is also invertible.

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