Let S and T denote linear transformations of a real finite dimensional vector space V. Suppose S(T(v))=T(S(v)) for all v that is in V.
(a) Prove that T maps each eigensapce of S onto itself.
(b) Suppose that each S and T may be represented by diagonal matrices. Prove that there exists a basis for V with respect to which both S and T are given by diagonal matrices simultaneously.
i can do part a) but i need a help on b). i dont even know if a) could be useful to prove b). please help.