Choose some j\in\{1,\dots,n\}. If the right ideal (1-k_j) R were proper, then it would be contained in a maximal right ideal M\neq R and both 1-k_j and k_j would belong to M, leading to a contradiction (note that \operatorname J(R)\subseteq M by the definition of the Jacobson radical). Thus (1-k_j)R=R and 1-k_j has a right inverse (1-k_j)^{-1} in R. We have
