  Molybdenum trioxide (MoO$_3$) in-plane anisotropy has increasingly attracted
the attention of the scientific community in the last few years. Many of the
observed in-plane anisotropic properties stem from the anisotropic refractive
index and elastic constants of the material but a comprehensive analysis of
these fundamental properties is still lacking. Here we employ Raman and
micro-reflectance measurements, using polarized light, to determine the angular
dependence of the refractive index of thin MoO$_3$ flakes and we study the
directional dependence of the MoO$_3$ Young's modulus using the buckling
metrology method. We found that MoO$_3$ displays one of the largest in-plane
anisotropic mechanical properties reported for 2D materials so far.
