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The group $GL(2,Z)$ acts in a natural way on the set of pairs of $n\timesn$-matrices determined up to a simultaneous conjugation. For $n=3$ we writeexplicit formulas for action of generators of $GL(2,Z)$ in the terms ofspectral data of matrices, i.e., spectral curves and line bundles.

Spectral data for pairs of matrices of order 3 and action of the group $GL(2,Z)$