 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2003/paper-1/5/b/i/solution

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

Take

A = B = I_{2}

det (A + B) = det (2 I_{2}) = 4

, whereas

det A + det B = 2

. This proves that the determinant is not additive. Being a multilinear map of separate columns does not imply additivity in the entire matrix.

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