已知 $A=\left[\begin{array}{ll}2 & 1 \\ 1 & 0\end{array}\right]$ ，且对所有正整数 $n \geq 2$ ，令 $A^n=\left[\begin{array}{ll}a_n & b_n \\ c_n & d_n\end{array}\right]$ 。试选出正确的选项。
A
$b_2 < c_2$
B
$A^2=2 A+\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
C
$c_{n+2}=c_{n+1}+2 c_n$
D
$\left[\begin{array}{ll}a_n & b_n \\ c_n & d_n\end{array}\right]\left[\begin{array}{l}0 \\ 1\end{array}\right]=\left[\begin{array}{l}b_{n+1} \\ d_{n+1}\end{array}\right]$
E
$d_{2 n}-a_{2 n}=\left(d_n\right)^2-\left(a_n\right)^2$
F