By antisymmetrizing the action of grasp and binor identity, it is proved that the spin network states of 3-valent and any-valent are the eigenstates of the volume operator and the area operator, respectively. The formulas 2-32l3p∑ipσpτpρ and 2-1l2p∑jpl(j) for calculating the eigenvalue spectrums of volume and area, respectively, are obtained.