Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Digital systems, linear algebra, introduction to formal proof / 5 / b / i / Solution

Transpose both inverse identities, using reversal of multiplication under matrix transposition:

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

Thus $(A^{T})^{- 1} = (A^{- 1})^{T}$ , by uniqueness of the matrix inverse.

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