Let be the linear transformation given by where . Demonstrate that T is unitary if and only if .

If is a unidimensional vector space, demonstrate that the only unitary linear transformations are the one given previously. In particular, if is a unidimensional vector space, there exist only 2 orthogonal transformations: and .

Attempt: Not much. I want to prove first.

If T is unitary, then . I don't know how to go further, I must show that this implies that .

Hmm... .

Stuck here.