Find all the sets $A$ and $B$ such that $P(A \times B)=P(A)\times P(B)$

Question

The last question in my exercise is to find all sets such that $P(A \times B)=P(A)\times P(B)$, where $P()$ denotes the power set. But I'm not sure how to go about finding sets which satisfy the equation; what I've tried so far is looking at the elements of each set, but $P(A\times B)$ has sets of ordered pairs as elements and $P(A)\times P(B)$ has ordered pairs of sets as elements, so there are no sets which satisfy the equation; is this correct?

Answer 1

The set $P(A)\times P(B)$ has $(\emptyset,\emptyset)$ for element while $P(A\times B)$ doesn't