 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2021/paper-1/18/a/i/solution

The matrix trace is the sum of diagonal entries:

Tr M = a^{2} + 1 - 1 = a^{2} .

Consequently

a = \pm 3, b \in R arbitrary .

The first diagonal entry is

a^{2}

in the original PDF.

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