Operations making non-context-free languages regular

Question

1. If $A$ is a non-context free language, is $A^*$ a regular language?
2. If $A$ is a non-context free language and $B$ is a regular language, is it possible that their concatenation is a regular language?

Answer 1

Let $A$ be $\{a^p\mid p\text{ is prime}\}$. Let $B$ be $\{a\}^*$.

Both $A^*$ and $A\circ B$ are regular. $A^*$ is $\epsilon+aaa^*$ and $A\circ B$ is $aaa^*$.