Prove/ Disprove: If $L$ is a CFL then $A(L)$ is a CFL too
A simple first step. 

Consider any language $K \subseteq \{a,b\}^*$, and let $1,2$ be two new symbols. Let $L = 1\cdot \{a,b\}^* \cdot 2 \cup  2 \cdot  K \cdot 1$.

What if $1x2\in A(L)$?