The stability of the Equilibrium Point 0

Let  A a 2*2 Matrix .

1.  If all the eigenvalues of  A have negative real part , then 0 is sink (asymptotical stable ) .
2. If all the eigenvalues of A have positive real part , then 0 is source (unstable) .
3. If  A has at least one eigenvalues with positive real part and at least one eigenvalues with negative real part and and none of the eigenvalues has a zero real part , then 0 is saddle (unstable ).
4. If all the eigenvalues of A have zero real parts then 0 is center (stable but not asymptotical stable ) .