Let U and A be two linear maps related by U=e^iA. Show that U is unitary if A is self-adjoint. Give a counterexample to show that U can be unitary if A is not self-adjoint.
The Attempt at a Solution
OK, so I had no problem with the first part. It's easy to show that U dagger=U inverse. However, I'm having some trouble coming up with a counter example for the second part. I tried something anti-Hermitian, but that just shows that U is self-adjoint, not that it is unitary.