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 / 4 / c / Solution

With the two diagonal matrices from the preceding part, write $D_A=PA{P}^{-1}$ and $D_B=PB{P}^{-1}$. Their diagonal products agree entry by entry, so $D_A{D}_B=D_B{D}_A$. ThereforeHence simultaneous diagonalization implies that $A,B$ are commuting operators.