Let $a,b \in F$, $0 \leq n \in \mathbb{Z}$ and let $A_n = [a_{ij}] \in M_n(F)$.
Define $$A_n=\begin{cases} a,&\text{if}\enspace j=i+1\\ b,&\text{if}\enspace j=i-1 \\ 0,&\text{otherwise} \end{cases}$$
How can i establish the formula for the $\text{det}A_n$?