Let $A_1$ and $A_2$ be context$-$free languages over $$ and $G_1$ and $G_2,$ respectively, be the grammars

generating the languages, that is$,L(G_1)=A_1$ and $L(G_2)=A_2.(5$ points$)$

$($a$)$ Determine the grammar $G$ that generates the language $A_2$@$A_1.$

$($b$)$ Support your answer in $($a$)$ by proving that $L(G)=A_2{A}_1.$