 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2010/ia/paper-1/7b/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

t I

commutes with

A

, so

A^{2} - t^{2} I = (A - t I) (A + t I) .

Taking determinants and using their multiplicativity gives, with the specified characteristic polynomial convention,

χ_{A^{2}} (t^{2}) = det (A - t I) det (A + t I) = χ_{A} (t) χ_{A} (- t) .

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