Using the power-Lanczos method me study the ground state (GS) properties of the two-dimension infinite U Hubbard model (IUHM) for 8 x 8 and 10 x 10 square lattices. We found that the charge structure factor of IUHM is very similar to that of hard core boson (ZZB). By comparing the GS energies of IUHM and spinless fermion wedetermined the critical hole density 6, ~ 0.26 above which the Nagaoka state becomes unstable.