State Elimination

Begin a two$-$state DFA with input alphabet $\{$a$,$ b$\}$ whose language is a$*.$ Make an equivalent four$-$state r$.$e$.-$NFA by adding a new initial and final state. Apply state elimination to this r$.$e$.-$NFA to form a regular expression. No matter which state is eliminated first, the resulting regular expression is a$*.($Here we are allowed to use the identity property of $\backslash$lambda $.)$ true or false