Prove that $id_{\vec{X}} + f’ + (f’)^{2}+\cdots+(f’)^{n}=0$, where $f:X\to X$ is the bijective affine transformation

Question

If $X$ is an affine $n$ dimensional space over a field of characteristic bigger than $n+2$ and $(A_{0},A_{1},\ldots,A_{n})$ an affine frame of $X$, prove that $id_{\vec{X}} + f’ + (f‘)^{2}+\cdots+(f’)^{n}=0$, where $f:X\to X$ is the bijective affine transformation defined as $f(A_{0})=A_{1}$, $f(A_{1})=A_{2}$, \ldots , $f(A_{n})=A_{0}$. I know how to find the passing matrix of this function from one frame to another, but I am stuck at that equality. Any help?