Complement of $0^n1^n | n \in \mathbb{N}$
Since $0 \in A$ and $1 \in A$, any word $w \in \Sigma^*$ can be written has a concatenation of $n=|w|$ words $w_1, \dots, w_n$ such that each $w_i \in A$ (showing that $w \in A^*$). In order to do so it suffices to pick $w_i$ as the $i$-th character of $w$, i.e., $w_i$ is either $0$ or $1$.