The analysis of high precision and high statistics 3H spectra offers the possibility to search for signature due to the existence of keV sterile neutrino. The Microcalorimeter Arrays for a TRItium eXperiment, MATRIX has been conceived to search for a tiny kink in a high statistics and high energy resolution calorimetrically measured 3H spectrum which can be related to the emission, during beta decay, of keV sterile neutrinos mixing with active neutrinos. Large arrays of low temperature metallic magnetic calorimeters, in which each pixel encloses a 3H activity of the order of 10 Bq, will be read out using the microwave SQUID multiplexing technique. Such an experiment presents several challenges: first to demonstrate that 3H loaded detectors can be reliably fabricated and that could achieve good performance in terms of energy resolution and time resolution, second to provide a multiplexed readout scheme able to allocate enough bandwidth per channel and with reduced additional noise. In this project, we have defined the seeds for the development of the MATRIX experiment.