  We study the connectedness of the planar self-affine sets
$T(A,{\mathcal{D}})$ generated by an integer expanding matrix $A$ with
$|\det(A)|=3$ and a non-collinear digit set ${\mathcal D}=\{0, v, kAv\}$ where
$k\in {\mathbb Z}\setminus\{0\}$ and $v\in {\mathbb Z}^2$ such that $\{v, Av\}$
is linearly independent. By checking the characteristic polynomials of $A$ case
by case, we obtain a criterion concerning only $k$ to determine the
connectedness of $T(A,{\mathcal{D}})$.
