Explain your reasoning and show calculations$/$steps$,$ please. This task is taken from "The Greedy Algorithm" $($Dieter Jungnickel$).$

Let $G=(V,E)$ be a connected graph which is not a tree.

a$)$ Prove that subsets of $E$ which contain at most one cycle form a matroid on E$.$

b$)$ Would the same hold if we allowed a maximum of two cycles?