Show that A** subset of A*, where A is a regular language I do not understand the proof for this. I know that every word in $(A^*)^*$ is made up of words from $A^*$, and that this is made up from words in $A$. But how does this help with showing that $(A^*)^*$ is a subset of $A^*$.
Knowing that $A$ is regular is not relevant. 

Hint. Just replace "made up of words of $A^*$" by "is a concatenation of words of $A^*$" in your sentence and you will have the answer.