  One of the most important sources for space-borne gravitational wave
detectors such as TianQin and LISA, is the merger of massivie black hole
binaries. By analyzing the inspiral signals, we can probe the characteristics
of massive black holes, including the spin-induced multipole moments. By
verifying the relation among mass, spin, and quadrupole moment, the no-hair
theorem can be tested. In this work, we analyed the capability of probing the
spin-induced quadrupole moment with the inspiral signal of massive black hole
binaries using space-borne gravitational wave detectors. Using the Fisher
information matrix, we find that the deviation of the quadrupole moment can be
constrained to the level of $10^{-1}$, and events with higher mass ratios will
provide a better constraint. We also find that the late inspiral part will
dominate the result of parameter estimation. The results of Bayesian analysis
indicate that the capability will be significantly enhanced by considering
higher modes. We also calculate the Bayes factor, and the results indicate that
the model of a black hole and a Boson star can be distinguished without a
doubt.
