1. The problem statement, all variables and given/known data Suppose V is a unitary space [over C] and T: V -> V is a normal transformation that satisfies T-1=-T. Prove that T is unitary transformation. 2. Relevant equations I know that T is unitary if and only if it is normal and the absolute value of its eigenvalues is 1. [*2] 3. The attempt at a solution T-1=-T so T2=-I, now suppose a is an eigenvalue of T so T2v=a2v=-Iv what in turn means [itex]a=\pm 1[/itex]. So from [*2] we can conclude that T is unitary. Have I missed something?