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## Homework Statement

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.

## Homework Equations

I know that T is unitary if and only if it is normal and the absolute value of its eigenvalues is 1. [*2]

## The Attempt at a Solution

T

^{-1}=-T so T

^{2}=-I, now suppose a is an eigenvalue of T so T

^{2}v=a

^{2}v=-Iv what in turn means [itex]a=\pm 1[/itex].

So from [*2] we can conclude that T is unitary.

Have I missed something?