 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2003/paper-1/5/a/ii/solution

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

The two-by-two matrix inverse formula gives

M^{- 1} = (- 4 3 3 - 2), N^{- 1} = (4 - 1 - 3 1), (MN)^{- 1} = (- 25 7 18 - 5) .

Multiplication in the reversed order gives

N^{- 1} M^{- 1} = (- 25 7 18 - 5) = (MN)^{- 1} .

The order reversal is needed because applying the inverse undoes the original two linear maps in reverse sequence.

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