 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-2/3/solution

2 \cdot 4 - 3 \cdot 1 = 5 \neq = 0

, so the matrix inverse exists. Using the two-by-two adjugate matrix formula gives

A^{- 1} = \frac{1}{5} (4 - 3 - 1 2) .

Multiplication on either side gives the identity matrix, which also checks the signs of the off-diagonal entries.

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