64 Checking the solution, concluded

Since $A$ is a companion matrix, we have

$$det(sI-A)=s^3+6s^2+8s-2$$

so

$$T(s)=\frac{C\text{adj}(sI-A)B}{det(sI-A)}=\frac{1+3s+2s^2}{s^3+6s^2+8s-2},$$

as required.