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We obtain defining relations of the algebra of invariants of the classical subgroups of GL2(C) acting by simultaneous conjugation on m-tuples of 2×2 complex matrices. The sets of defining relations look uniformly for all m≥2 and are derived by translation of classical results on invariant theory of orthogonal groups in the language of 2×2 matrix invariants, combined with arguments of representation theory of the general linear group GL m (C) and ideas coming from the theory of algebras with polynomial identities.