 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2007/paper-2/section-b/7/a/iii/solution

True. Distribute the matrix product while retaining its order:

A^{- 1} (A + B) B^{- 1} = A^{- 1} A B^{- 1} + A^{- 1} B B^{- 1} = B^{- 1} + A^{- 1} = A^{- 1} + B^{- 1} .

Only addition is commuted; no commutation of

A

and

B

is assumed.

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