 Solution

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

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

A_{ji}

denotes the matrix obtained by deleting row

j

and column

i

adj (A)_{ij} = (- 1)^{i + j} det A_{ji} .

For nonsingular

A

adj (A) = det (A) A^{- 1} .

Therefore, when

A

and

B

are nonsingular,

adj (A B) = det (A) det (B) (A B)^{- 1} = det (B) B^{- 1} det (A) A^{- 1} = adj (B) adj (A) .

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