 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2005/ii/paper-2/19g/iii/solution

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

A

A^{*} A = diag (∣ Z (g_{j}) ∣)

. Taking determinants gives

∣ det A ∣^{2} = det (A^{*} A) = j \prod ∣ Z (g_{j}) ∣.

In particular its determinant is nonzero.

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