Can a transformer operate on DC?

A transformer cannot operate on a steady or unchanging dc voltage such as that of a battery. It requires a voltage that rises and falls. Since an ac voltage not only changes its magnitude but its direction as well, it is used to operate the transformers.
However, a transformer will operate from dc voltage if this voltage also undergoes changes. Transformers used for audio amplifiers work on pulsating dc voltage. The main thing which causes the transformer to work is the change in voltage. It is immaterial whether the voltages change from positive to negative values or from positive to zero values.