In this paper we consider a two dimensional dynamical system with arbitrary piecewise constant parameters described by a linear homogeneous differential equations system with discontinuous coefficients. For such a system the fundamental solution matrix in the analytical form in elementary functions is found. The theorem saying that this matrix is the finite sum of the unimodular matrices with the certain influence coefficients is proved. The results allow us to carry out qualitative analysis of the corresponding dynamical systems, solve inverse problems, investigate the conditions for the oscillation stabilities. Obviously, the results can be used in theory of inhomogeneous and non-linear systems.