Please answer all parts

3. (Commutator) Commutators play a major role in quantum mechanics as they identify properties of a system we can simultaneously know. Commutators can be evaluated by operating them on a generic function, f(x). Evaluate the commutator, [A^,B^], for each of the following pairs of operators: a. A^= square, B^= square root b. A^=x;B=idxd c. A^=x2;B^=dx2d2 d. If two operators commute, show they must share a common set of eigenfunctions. e. Your answer to part d implies something key about operators that represent physical quantities. If two operators that represent physical observables of a system commute, what does that imply regarding the precision to which we can know these quantities? Hint: McQuarrie \& Simon Textbook Chapter 4.6