Let $\displaystyle V=R^2 $ and define $\displaystyle T\in L(V) $ as the 90-degree rotation operator given by $\displaystyle T(x,y)=(-y,x) $ where $\displaystyle x,y \in R $ are the components of a vector in V.

a- show that T is normal

b-T does not have any eigenvalues in R.

Thanks