= Solution
The squared <angular momentum operator> and one selected component are <commuting operators>, so a complete set of common <eigenfunctions> can be chosen: for the $z$ component these are the usual $|j,m\rangle$ <angular momentum eigenstates>. Distinct components do not have a common complete <eigenbasis>, because their <commutator> is another nonzero component. A $j=0$ state is an exception in which all components vanish; noncommutation does not forbid every individual common <eigenfunction>.
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