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In this paper we present representation of finite effect algebras by matrices. For each non-trivial finite effect algebra $E$ we construct set of matrices $M\left(E\right)$ in such a way that effect algebras $E_1$ and $E_2$ are isomorphic if and only if $M\left(E_1\right)=M\left(E_2\right)$. The paper also contains the full list of matrices representing all nontrivial finite effect algebras of cardinality at most $8$.