Abstract
Let A n = Circ ( F 1 , F 2 , … , F n ) and B n = Circ ( L 1 , L 2 , … , L n ) be circulant matrices, where F n is the Fibonacci number and L n is the Lucas number. We prove that A n is invertible for n > 2, and B n is invertible for any positive integer n. Afterwards, the values of the determinants of matrices A n and B n can be expressed by utilizing only the Fibonacci and Lucas numbers. In addition, the inverses of matrices A n and B n are derived.
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