We propose some general approach to studying the problem for the representabilityof every element $ a $ in a field $ F $ in the form $ a=f+g $ , with $ f^{q_{1}}=f $ and $ g^{q_{2}}=g $ , where $ q_{1},q_{2}>1 $ are fixed naturals, to imply the analogous representabilityof every square matrix over $ F $ . Asan application, we describe the fields and commutative rings with $ 2\in U(R) $ suchthat every square matrix over them is the sum of a $ q_{1} $ -potent matrix and a $ q_{2} $ -potentmatrix for some small values of $ q_{1} $ and $ q_{2} $ .
