 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/ii/solution

True. Using the same transpose identity and

X^{T} = - X

gives

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

The final equality follows by multiplying

- X

and

- X^{- 1}

in either order and obtaining the identity. Thus the inverse is a skew-symmetric matrix as well. The invertibility hypothesis is retained throughout.

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