 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/ii/solution

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

Expanding the trace of the product and exchanging the two finite summation indices gives

Tr (A B) = \sum_{i, j} a_{ij} b_{ji} = \sum_{j, i} b_{ji} a_{ij} = Tr (B A) .

Scalar entries commute even though the matrices need not.

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