 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ia/paper-1/2b/a/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

M^{T} J M = J

gives

det (M)^{2} det J = det J .

Since

det J = - 1 \neq = 0

, one has

det (M)^{2} = 1

, and hence

det M = 1 or det M = - 1 .

Both values occur, for example for

M = I

and

M = diag (1, - 1)

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