Let \(A\) be an algebra. A (not necessarily additive) map \(\varphi\colon A\to A\) is called a 2-local automorphism if for every pair \(a,b\in A\) there exists an automorphism \(\sigma_{a,b}\) of \(A\) such that \(\varphi(a)=\sigma_{a,b}(a)\) and \(\varphi(b)=\sigma_{a,b}(b)\). 2-local derivations are defined analogously.
The paper considers the matrix algebra \(A=M_n(K)\) where \(K\) is a finite-dimensional division algebra over its center and \(\text{char}(K)\neq 2\). It is shown that a \(2\)-local automorphism of \(A\) is necessarily an automorphism or an antiautomorphism. Moreover, the second possibility may occur only when \(n=1\). Similarly, 2-local derivations of \(A\) are derivations.