MATISSE, the VLTI 2 nd generation spectro-interferometric L, M and N bands imager, has been commissioned from March 2018 to March 2020. It is open to the General User since April 2019. A complete analysis of its performances is given in this paper for MATISSE standalone (with UTs and ATs) and for the GRAVITY for MATISSE (GRA4MAT) mode (with ATs) where the GRAVITY fringe tracker is used to stabilize the fringes in MATISSE and hence improve its sensitivity and spectral coverage at high spectral resolution. This paper presents the key operation parameters of MATISSE and decomposes its performances in fundamental precision per spectral channel for all measurements and in broad band calibration errors on the accuracy of visibility and closure phase. It is intended to give the user a full description of the different errors that must be considered and weighted in the model fitting and image reconstruction. The first image reconstructions achieved by MATISSE are discussed. The performances demonstrated here in the full very broad spectral domain of MATISSE open a very large domain of scientific applications that includes but strongly expands quantitatively and qualitatively the initial science program of the first generation instrument MIDI and, combined with GRAVITY, offers an extremely powerful tool to characterize the temperature and composition of dusty and molecular components of YSOs, AGNs and evolved stars.