Proving Stability and Asymptotic Stability of Homogeneous Equations

Hi,
Using these definitions:

A homogeneous equation with constant coefficients is said to be stable if all solutions remain bounded as t-->infinity

A homogeneous equation with constant coefficients is said to be asymptotically stable if all solutions converge to the zero solution as t-->infinity

I'm trying to prove these two statements:

1) The system is stable if and only if for every root $\lambda = \alpha + i\beta$ of the characteristic polynomial, $0 \geq \alpha$ and $\alpha < 0$ if the multiplicity of lambda is bigger than one.

2) The system is aymptotically stable if and only if for every root $\lambda = \alpha + i\beta$ of the characteristic polynomial, $\alpha < 0$ .

Thanks a lot!