Provide all subsets of $A$ so that $A^{**}($Kleene closure$)$ is a finite set.

Construct an non$-$deterministic automaton $($NFA$)M$ that accepts the language $L(M)=\{\{(ab{)}^n|n1\}\{(abb{)}^n|n1\}\}$ over $=\{a,b\}(2$ points$).$ Convert M into a deterministic automaton $($DFA$)$ that accepts the same language $(3$ points$).$ Note, a DFA state always has exactly one $"$a$"$ and one $"$b$"$ outgoing transition.