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In this paper we derive the recurrent formulae for any integers powers of certain asymmetric matrices five order which covers also constans tridiagonal matrices and some asymmetric (and symmetric) pentadiagonal matrices. Since we find also the Binet's formulae for the elements of the powers of these matrices, it is possible to operate with powers series of these matrices. We note that this method is alternative to the Jordan method decomposition.

Integers Powers of Certain Asymmetric Matrices