G. BELYAVSKAYA
We establish connection between product of two matrices of order k k over a eld and the product of the k-mappings corresponding to the k-operations, de ned by these matrices. It is proved that, in contrast to the binary case, for arity k 3 the components of the k-permutation inverse to a k-permutation, all components of which are polynomial k-quasigroups, are not necessarily k-quasigroups although are invertible at least in two places. Some transformations with the help of permutations of orthogonal systems of polynomial k-operations over a eld are considered.
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