Hi promach,
Mathematically speaking, a unitary matrix is one which satisfies the property ^* = ^{-1}. Re-arranging, we see that ^* = , where is the identity matrix.
Inserting the matrix into this equation, we can then see that any column dotted with itself is equal to unity. Conversely, if any column is dotted with any other column, the product is equal to 0.
So if we take your 2x2 scattering matrix and look at some examples, we would find that |S12|^2 + |S22|^2 = 1. If the network is reciprocal, then S12 = S21. We would also have that |S11|^2 + |S21|^2 = 1 and (S11*)(S12) + (S21*)(S22) = 0.