 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-2/11/d/solution

The trace is the sum of the eigenvalues, counting multiplicity, while the determinant is their product:

tr A = 1 - 2 + 1 = 0 = 4 - 2 - 2, det A = 16 = 4 (- 2) (- 2) .

A direct expansion along the middle row checks the latter:

(- 2) (1 - 9) = 16

 New to topics? Read the docs here!