 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2008/paper-1/18/b/iii/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

Apply the preceding trace identity first to the pair

A B, C

and then to

C A, B

Tr (A BC) = Tr (C A B) = Tr (BC A) .

This is invariance under cyclic permutation. It does not assert invariance under arbitrary rearrangement of the matrices.

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