Let
$$A\in M_2({\mathbb {Z}})$$
be an expanding integer matrix and
$$D=\{d_1={\textbf{0}},d_2,d_3\}\subset {\mathbb {Z}}^2$$
. It follows from Hutchinson (Indiana Univ Math J 30:713–747, 1981) that the generalized Sierpinski self-affine set
$${\textbf{T}}(A,D)$$
is the unique compact set determined by the pair (A,D) satisfing the set-valued equation
$$A{\textbf{T}}(A,D)=\bigcup _{i=1}^3({\textbf{T}}(A,D)+d_i)$$
. In this paper, we show that Fuglede’s conjecture holds on
$${\textbf{T}}(A,D)$$
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