Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Digital systems, linear algebra, introduction to formal proof / 1 / d / Solution

Define the characteristic polynomial using $p(\lambda )=\det (\lambda I-P)$, where $I$ is the identity matrix. Expanding the determinant along the first row givesThus the characteristic equation isThe convention $\det (P-\lambda I)$ changes the sign of this cubic polynomial but gives the same roots.