Question $2-$Pushdown Automata and context$-$free languages

Consider alphabet $2=\{$a$,$b$,$ #; and the language

B$=\{$wEL$*|$ w$=$a$"$#n#a$"$ for some n $$ N$\}.$

$($a$)$ Prove that B is not context$-$free. $($b$)$ Explain how the following PDA P operates on words over & and show that all

words in B are accepted by this PDA.

a$,$ a

b$,$

a$,$ b $$

$,$ $

#$,$

#$,$

E$,$ $ $$

$90$

$91$

$92$

$93$

$94$ b$,$$ $$ $

$6,66$

$,$ b

$95$

$($c$)$ Identify the language L$($P$)$ of the above pushdown automaton.

$($d$)$ Provide a context$-$free grammar for the language L$($P$).$