 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2017-resit/10/a/i/solution

(A B) (B^{- 1} A^{- 1}) = A (B B^{- 1}) A^{- 1} = I, (B^{- 1} A^{- 1}) (A B) = B^{- 1} (A^{- 1} A) B = I .

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

The order is reversed;

A^{- 1} B^{- 1}

does not generally work because matrix multiplication need not be commutative.

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