Answer:
Assuming that you refer to [tex]A^2[/tex] as the Cartesian product of A with A, then remember that the cartesian product of two sets A and B is the set
[tex]A\times B=\{(a,b): a\in A, b\in B\}[/tex]
Then, if [tex]A=\{0,\{1\}\}[/tex],
[tex]A^2=A\times A=\{(0,0), (0,\{1\}),(\{1\},0),(\{1\},\{1\})\}[/tex]
