The Fibonacci number sequence is given by
$$F_n = F_{n−1} + F_{n−2},\ n \ge 2,\\F_0 = F_1 = 1$$
Suppose we write two consecutive Fibonacci numbers in the form of a $2 \times 1$ matrix $f$, where
$$ f = \begin{pmatrix} f_n\\ f_{n + 1}\\ \end{pmatrix}. $$
Show that there is a $2 \times 2$ matrix $A$ such that when $f$ is multiplied by $A$ we get
$$ A\begin{pmatrix} f_n\\ f_{n + 1}\\ \end{pmatrix} = \begin{pmatrix} f_n\\ f_{n + 1}\\ \end{pmatrix}. $$
Hint: What is $F_{n+1}$ in terms of $F_n$ and $F_{n−1}$?