 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-1/6/i/solution

M^{T} = - M

. Invariance of the determinant under transpose gives

det M = det M^{T} = det (- M) = (- 1)^{n} det M .

For odd

n

2 det M = 0

, so $det M = 0$ over the real or complex numbers.

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