A=(({{0, 2}, {1, 3}}))
Eigenvalues[A]
Fi=Eigenvectors[A]
inFi=Inverse[Fi]

Fi.(({{(E^((1/2) (3+(Sqrt[17]))s)), 0}, {0, (E^((1/2) (3-(Sqrt[17]))s))}})).inFi//Simplify