Let f,g End(V) be endomorphisms of an n-dimensional vector space V over K, matrices whose minimal polynomial splits completely over K. Show that if fog=gof, then there is a basis of V in which the matrices of both ƒ and g are upper triangular. Use this to deduce that two commuting matrices A, B over C (or an algebraically closed field K) can be simultaneously put in an upper triangular form.