 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2008/paper-1/18/a/iii/solution

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

T = diag (1, 0, 0)

. Multiplying on the left retains the first row of

S

, while multiplying on the right retains its first column. Thus

TS = 100000100, ST = 101000000 .

Their

(1, 3)

entries differ, so this is an explicit example of noncommuting matrices.

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