The tangent space at a point of two-dimensional torus

Question

Consider the hyperbolic toral automorphism $A : T^2 \to T^2$ $$A (x, y) = (2x + y, x + y) \; \text{mod} \; 1.$$ Let $M$ be a Riemannian manifold.

Can someone explain me who is the tangent space $T_x M$, for every $x \in T^2$ ?

Thank you!