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In this paper, we investigate Min matrices [Formula: see text] and Max matrices [Formula: see text] whose entries are [Formula: see text] and [Formula: see text], respectively, where [Formula: see text] and [Formula: see text]. By utilizing combinatorial identities, we derive the characteristic polynomials of M and U. Additionally, relationship between generalized Fibonacci numbers and the characteristic polynomials of these matrices is established. Finally, some examples are given to illustrate our results.