$[15$ Points$]$ Let $G$ be the following CFG in which $S$ is the start variable:

$SAB|aB||$

$A$aab$|||$

$B$bbA

$($a$)(5$ Points$)$ Using the procedure discussed in the class, convert $G$ into an equivalent grammar in Chomsky Normal Form $($CNF$).$

$($b$)(5$ Points$)$ Find an equivalent grammar to $G$ in Greibach Normal Form $($GNF$).$

$($c$)(5$ Points$)$ Suppose we modify the original grammar $G$ as follows: remove the $-$production $A$ and instead add the unit producion $AA.$ Let us call the resulting grammar as $G^{\text{'}}.$ Convert $G^{\text{'}}$ into CNF$,$ and simplify, if possible. Also describe in English the language $L(G^{\text{'}}).$