In this paper we solve the following system of difference equations {equation*} xₙ₊₁={zₙ₋₁}{a+by_nzₙ₋₁}, yₙ₊₁={xₙ₋₁}{a+bz_nxₙ₋₁}, zₙ₊₁={yₙ₋₁}{a+bx_nyₙ₋₁}, n∈ N₀ {equation*} where parameters $a, b$ and initial values x₋₁,x₀,y₋₁,y₀,z₋₁,z₀ are nonzero real numbers, and give a representation of its general solution in terms of a specially chosen solutions to homogeneous linear difference equation with constant coefficients associated to the system.
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Halim et al. (2020) studied this question.