Following the idea of using first-order time derivatives, this paper presents a general recurrent neural network (RNN) model for online inversion of time-varying matrices. Different kinds of activation functions are investigated to guarantee the global exponential convergence of the neural model to the exact inverse of a given time-varying matrix. The robustness of the proposed neural model is also studied with respect to different activation functions and various implementation errors. Simulation results, including the application to kinematic control of redundant manipulators, substantiate the theoretical analysis and demonstrate the efficacy of the neural model on time-varying matrix inversion, especially when using a power-sigmoid activation function.