For 2x2: \[\lambda^2-Tr(A)\lambda+det(A)=0\]
For 3x3: \[-\lambda^3 + Tr(A)\lambda^2 +Prop(A)\lambda + det(A) = 0\]
Where \[Prop(A)=a_{21}a_{12}+a_{31}a_{13}+a_{32}a_{23}-a_{11}a_{22}-a_{22}a_{33}-a_{11}a_{33}\]
Not sure what this relates to at this stage.