 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2008/ii/paper-1/24h/a/solution

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

The determinant is continuous and

G L (n) = det^{- 1} (R ∖ {0})

is open in

M (n) ≃ R^{n^{2}}

. Every open subset inherits the ambient smooth charts, so it is a submanifold and

dim G L (n) = n^{2} .

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