I was attempting this question:
Consider $A \ne \varnothing$, where the number of subsets of $A$ is the same as the number of elements of $A\times A$. Determine the number of elements in $A$.
Because $\varnothing$ is naturally a subset of $A$ and in this question, it is clearly specified $A \ne \varnothing$, therefore can it be concluded that the number of elements is $A^n$?
Thank you in advance!