Unitary is UU*=I

U* is transpose conjugate

Prove that if a matrix U is unitary, then all eigenvalues of U have absolute value of 1.

$\displaystyle Uv= \lambda v $

$\displaystyle U^* Uv=\lambda U^*v$

$\displaystyle v= \lambda U^* v$

$\displaystyle v/\lambda=U^* v$

so v is also a eigenvector for U* with eigenvalue of $\displaystyle 1/\lambda$.

Not sure how to continue?

any help would be appreciated

Thanks in advance