$\newcommand{\End}{\operatorname{End}}$

let $R$ be a local ring, $\varphi\in \End(R_{R}^{2})$, $\overline{\varphi}\in \End(\overline{R}_{\overline{R}}^{2})$, $\overline{R} =R/J(R)$ , $J(R)$= Jacobson radical $R$. where neither $\varphi$ nor $1-\varphi$ is invertible. Why neither $\overline{\varphi}$ nor 1- $\overline{\varphi}$ is invertible in $\End(\overline{R}_{\overline{R}}^{2})$ ?