Past exam of the year 1 of the computer science course of the University of Oxford / 2022 / Digital systems, linear algebra, introduction to formal proof resit / 5 / e

For scalar $a=A\ne 0$, part (c) givesThe numerator is strictly positive for every real $a$, and the denominator is nonzero. Therefore $B\ne 0$ and hence $B$ is invertible. This proof uses the order structure of the real scalars; it does not say that the matrix $A^2+A+I$ must be nonsingular in higher dimension.