The statement:
Consider the system $x'=A(t)x$, where $A(t)$ is a periodic matrix with period T. If $|\lambda_i|=1$ then the corresponding Jordan block to $e^{TR}$ is diagonal. The constant matrix R comes from the general Floquet solution to the system: $x(t)=P(t)e^{tR}x(\tau)$, where P(t) is a periodic matrix.
Attempt at proof:
$|\lambda_i|=1 <=>|e^{T\rho_i}|=1 <=>\rho_i$ is purely imaginary
Dilemma:
I don't know how to proceed from here. Somehow I am supposed to arrive at the conclusion that algebraic and geometric multiplicities are the same. But this is lost on me. If anyone has a poignant hint or a complete continuation I would be extremely thankful.