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Within the framework of the theory of the column and row determinants, weobtain explicit representation formulas (analogs of Cramer's rule) for theminimum norm least squares solutions of quaternion matrix equations ${\bf A}{\bf X} = {\bf B}$, $ {\bf X} {\bf A} = {\bf B}$ and ${\bf A} {\bf X} {\bf B} ={\bf D} $.

Explicit representation formulas for the minimum norm least squares solutions of some quaternion matrix equations