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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2006/paper-1/1/a/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2006 / Paper 1 / 1 / a / Solution by

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

For a matrix proportional to its transpose, applying the transpose twice gives

A^{T} = 5 A

and therefore

A = 25 A

. Over the real numbers or complex numbers,

24 A = 0

implies

A = 0.

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