Statement I: The permeability of a ferromagnetic material is independent of the magnetic fleld.

Statement II: Permeability of a material is a constant quantity.

The permeability of a ferromagnetic material is not independent of magnetic field. $\overrightarrow{\mathrm{B}}={\mathrm{\mu }}_{\mathrm{m}}{\overrightarrow{\mathrm{B}}}_0. {\mathrm{B}}_0$ is applied field. The total magnetic field $\overrightarrow{\mathrm{B}}$ inside a ferromagnet may be ${10}^3 \mathrm{or} {10}^4$ times the applied field ${\mathrm{B}}_0$. The permeability ${\mathrm{\mu }}_{\mathrm{m}}$ of a ferromagnetic material is not constant. neither the field $\overrightarrow{\mathrm{B}}$ nor the magnetization $\overrightarrow{\mathrm{M}}. \overrightarrow{\mathrm{M}}$ increases linearly with $\overrightarrow{\mathrm{B}}$. even at small value of ${\mathrm{B}}_0$. From the hysteresis curve, magnetic permeability is greater for lower field.