Statement I: Soft iron is used as transformer core.

Statement II: Soft iron has narrow hysteresis loop.

The core of a transformer undergoes cycles of magnetisation again and again. During each cycle of magnetisation, energy numerically equal to the area of the hysteresis loop is spent per unit volume of the core. Therefore, for high efficiency of transformer, the energy loss will be lesser if the hysteresis loop is of lesser area, i.e., narrow. That's why the soft iron is used as core, which has narrow hysteresis loop (or area of B-H curve is very small). Also soft iron (ferromagnetic substance) has high permeability, low retentivity, low coercivity and low hysteresis loss.