Can anyone find out an counter example to this unitary statement? If $A$ and $B$ are unitary, then $A+B$ is not unitary.
I think this statement is true .
I tried to find out counter example but I failed. 

The $0 \times 0$ matrix is unitary, thus it is a counterexample.
Exluding degenerate matrices, $1 \times 1$ matrices are the simplest; they're usually a good place to look for counterexamples, if you aren't trying to exploit noncommutativity.
A $1 \times 1$ unitary matrix is simply a complex number of absolute value $1$. So the question becomes, can you find three complex numbers of absolute value $1$ such that $x+y=z$?
(if you have trouble with this, try thinking what this would mean geometrically)
