Past exam of the year 1 of the computer science course of the University of Oxford / 2021 / Digital systems, linear algebra, introduction to formal proof / 5 / a / iii / Solution

Let $e_{ij}$ denote the matrix unit with one at position $(i,j)$ and zero elsewhere. The five inverses areThus each is the identity matrix with only the indicated off-diagonal matrix entry altered. These inverses reverse the corresponding row additions; no row scaling or permutation is involved.