 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2005/paper-2/9/a/solution

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

A real normal matrix satisfies

M M^{T} = M^{T} M

M^{T} = M

and both products equal

M^{2}

M^{T} = - M

and both equal

- M^{2}

. For an orthogonal matrix, both products are the identity. Thus each of the three classes consists of normal matrices.

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