 Solution

ID: 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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