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Hints: 1. Pure imaginary eigenvalues cause rotations, and complex ones cause spirals. 2. If both eigenvalues are zero, the matrix is nilpotent. Try drawing a phase space for a nilpotent matrix to match this one up. 3. If one eigenvalue is 0, then every vector will be parallel. 4. Ask yourself why some arrows flow in and some flow out.

Perhaps the easiest thing to do is to draw out the phase portraits as if the eigenvectors were the coordinate axes. All other matrices are skewed versions of this.

Realize finally that there are two similarity classes of matrices with both eigenvalues being 1.