  Electromagnetic properties of neutrinos, if ever observed, could help to
decide the Dirac versus Majorana nature of neutrinos. We show that the magnetic
moments of Majorana neutrinos have to fulfill triangle inequalities,
$|\mu_{\nu_\tau}|^2 \leq |\mu_{\nu_\mu}|^2 +|\mu_{\nu_e}|^2$ and cyclic
permutations, which do not hold for Dirac neutrinos. Observing a violation of
these inequalities, e.g. by measuring the magnetic moment of $\nu_\tau$ at
SHiP, would thus strongly hint either at the Dirac nature of neutrinos or at
the presence of at least one extra light sterile mode.
