How do I find the powerset of $A\cap B$? $A = \{0,1\}$ 

$B = \{1,2\}$ 

My Working : 

$P(A\cap B)= P(\{\varnothing, \{1\}\}) = \{\varnothing,\{1\},\{\varnothing,\{1\}\}\}$

But the correct answer is $P(A\cap B)= \{\varnothing , \{1\}\}$.
The intersection of $A$ and $B$ is simply $\lbrace 1 \rbrace$, which has only $\lbrace \rbrace$ and $\lbrace 1 \rbrace$ as subsets, and so the power set is $\lbrace\lbrace \rbrace, \lbrace 1\rbrace \rbrace$. The empty set is a subset of $A$ and $B$, but it is not a member of either set. Therefore, the empty set is not a member of $A \cap B$. Similarly, $\lbrace 1\rbrace$ is a subset of, not a member of, $A$ and $B$, so it is not a member of the intersection.
$P(A\cap B)=P(A)\cap P(B)$ as any subset of $A\cap B$ has to be a subset of both $A$ and $B$, and the converse is trivial.