 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-2/6/c/ii/solution

The contraction is

tr (A^{3})

. Since

A^{T} = - A

, transpose and invariance of the trace give

tr (A^{3}) = tr ((A^{3})^{T}) = tr ((- A)^{3}) = - tr (A^{3}) = 0.

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