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

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- Solution 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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