\b[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.

Solution

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

 Solution (source code)