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 $X^T=-X$ givesThe 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.