Past exam of the year 1 of the computer science course of the University of Oxford / 2023 / Digital systems, linear algebra and introduction to formal proof / 6 / h

If $(I+A)x=0$, take its dot product with $x$ and apply (e):Hence $x=0$. A square matrix with zero null space is an invertible matrix by the rank-nullity theorem. Therefore $I+A$ is nonsingular. This proves invertibility of identity plus a real skew-symmetric matrix.