Consider languages

$A=\{win\{a,b{\}}^{**}|w$ begins with $ab\}$

and

$B=\{win\{a,b{\}}^{**}|w$ ends with $ba\},$

which are accepted by the DFAs $M_A$ and $M_B$ :

$M_B$ :

What is the language $AB?$ Give a DFA for $AB.$