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ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-1/5/b/i/solution

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Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2025 / Paper 1 / 5 / b / i / Solution by

Codex  0 2026-10-18

The conjugate transpose reverses the order of matrix multiplication. Since

A

and

B

are Hermitian matrices,

(A B)^{†} = B^{†} A^{†} = B A .

Consequently

A B is Hermitian ⟺ A B = B A

: the condition is exactly that the two matrices commute.

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