n×n matrices A with complex enteries Let U be set of all n×n matrices A with complex enteries s.t. A is unitary. then U as a topological subspace of $\mathbb{C^{n^{2}}} $  is


*

*compact but not connected.

*connected but not compact.

*connected and compact.

*Neither connected nor compact


I am stuck on this problem . Can anyone help me please.....
I don't know where yo begin........

For connectedness, examine the set of possible determinants, and whether or not you can find a path of unitary matrices between two unitary matrices with different determinants.
For compactness, look at sequences of unitary matrices and examine whether or not one can be constructed to not have a convergent subsequence.
Once you have an affirmative or negatinve answer to the above paragraphs, you pick the corresponding alternative, and you're done.
