Suppose the eigenvalues are real, distinct, and non-zero.
[i] If both eigenvalues were positive, how would the equilibrium at (0,0) be classified?
[ii] If both eigenvalues were negative, how would the equilibrium at (0,0) be classified?
[iii] If one eigenvalue was negative, and one eigenvalue was positive, how would the equilibrium at (0,0) be classified?