 Solution

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

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

False in general. For symmetric matrices,

(A B)_{ji} = A_{jk} B_{ki} = B_{ik} A_{kj} = (B A)_{ij}

A B = B A

. For example,

A = (1000), B = (0110), A B = (0010)

has

(A B)_{12} = 1

and

(A B)_{21} = 0

despite both factors being symmetric.

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