 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/digital-systems-linear-algebra-introduction-to-formal-proof-resit/4/d/i/solution

True. Transposing the inverse identities shows

(X^{- 1})^{T} = (X^{T})^{- 1}

. If

X^{T} = X

, this becomes

(X^{- 1})^{T} = X^{- 1}

, exactly the symmetric matrix condition. The reasoning uses the matrix inverse and transpose identities, without assuming that different matrix factors commute.

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