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A technique to compute arbitrary products of a class of Fibonacci $2\times2$square matrices is proved in this work. General explicit solutions for nonautonomous Fibonacci difference equations are obtained from these products. Inthe periodic non autonomous Fibonacci difference equations the monodromymatrix, the Floquet multipliers and the Binet's formulas are obtained. In theperiodic case explicit solutions are obtained and the solutions are analyzed.

Products of 2X2 matrices related to non autonomous Fibonacci difference equations