How to find that the following set is connected and compact or not?

Question

Let $U$ denote the set of all $n\times n$ matrices $A$ with complex entries such that $A$ is unitary. Then $U$, as a topological subspace of $\mathbb{C}^{n^2}$ is,

1. Compact, but not connected.
2. Connected, but not compact.
3. Connected and compact.
4. Neither connected nor compact.

I know what the terms are but I am really not getting the idea how to solve this. Please help.