$14\mathrm{.}2$: Strings going to a state

Let M be a DFA with alphabet $\{$a$,$ b$\},$ state set $\{1,2,3\},$ start state $1,$ final state set $\{1,3\},$ and transition function given by $(1,$ a$)=1,$ $(1,$ b$)=2,$ $(2,$ b$)=$ $(3,$ a$)=2,$ and $(2,$ a$)=$ $(3,$ b$)=3.$ Then for any string w$,$$*(1,$ w$)=1$ if and only if w is in the language a$*.$