 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ia/paper-1/6a/a/solution

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

Using the convention of the question, the characteristic polynomial and characteristic equation are

χ_{A} (z) = det (A - z I), χ_{A} (z) = 0.

For

A = (a c b d),

one has

χ_{A} (z) = z^{2} - (a + d) z + (a d - b c) .

A^{2} - (a + d) A + (a d - b c) I = 0,

entry by entry. Thus

χ_{A} (A) = 0

2 \times 2

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