Why do transformer works only with AC Not with DC?

Because alternating current can produce mutual induction, DC is a direct current, no mutual induction hence not transformation of voltage, so that DC cannot be step up and step down. Transformer works on AC only , not on DC. Because :

1. There will not be mutual induction in Transformer in case of DC.
2. There is no frequency in DC. Finally, in AC Frequency then work T/F & frequency not available in DC then not work T/F. In DC convert step down or step up in buck boost converter