Theorem T11 Let FnF_nFn be the Fibonacci numbers. Then (Fn+1FnFnFn−1)=(1110)n ,n≥1.\begin{pmatrix} F_{n+1} & F_n \\ F_n & F_{n-1} \end{pmatrix}= \begin{pmatrix} 1 & 1 \\ 1 & 0 \end{pmatrix}^n \;, \quad n \geq 1. (Fn+1FnFnFn−1)=(1110)n,n≥1.