Past exam of the mathematics course of the University of Oxford / 2023 / Prelims / Mathematics I / 1 / b / ii / Solution

Write $A=I_3+N$, whereThe binomial theorem for commuting matrices applies because $I_{3}N=N{I}_3$. All terms of degree at least three vanish, so for every positive integer $n$,The same expression directly gives $A$ when $n=1$, so no small exponent is excluded.