Let \(V,W\) be linear spaces over a commutative field \(F\). Let \({\mathcal L}(V,W)\) denote the space of linear operators. For a subspace \({\mathcal S} \subset {\mathcal L}(V,W)\) and for an integer \(k>0\), the \(k\)-reflexive closure \(\text{Ref}_k({\mathcal S})\) is the set of operators \(T\) such that for any \(x=x_1\otimes x_2\otimes\dots\otimes x_k \in V^k\) (direct sum of \(k\)-copies of \(V\)), there exists an operator \(S_x \in {\mathcal S}\) such that \(T(x_i)=S_x(x_i)\) for \(1\leq i\leq k\). \({\mathcal S}\) is said to be \(k\)-reflexive if it coincides with the \(k\)-reflexive closure. Note that when \(k=1\), this is the usual notion of algebraic reflexivity. The \(k\)-reflexive defect of \({\mathcal S}\), denoted by \(\text{rd}_k({\mathcal S})\), is the dimension of the quotient space \(\text{Ref}_k({\mathcal S})| {\mathcal S}\). In this interesting paper, the authors show that when \(F\) has at least \(5\) elements, barring some exceptions, every two-dimensional \({\mathcal S}\) is algebraically reflexive.