 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2006/paper-1/6/a/i/solution

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

(a \times b) \cdot c = det (a, b, c) .

A cyclic permutation of its three columns is an even permutation, so it leaves the determinant unchanged. Thus

det (a, b, c) = det (b, c, a) = a \cdot (b \times c)

, proving the identity.

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