Polynomial system solving is one of the important area of Computer Algebra with many applications in Robotics, Cryptology, Computational Geometry, etc. To this end computing a Gröbner basis is often a crucial step. The most efficient algorithms [6, 7] for computing Gröbner bases [2] rely heavily on linear algebra techniques. In this paper, we present a new linear algebra package for computing Gaussian elimination of Gröbner bases matrices. The library is written in C and contains specific algorithms [11] to compute Gaussian elimination as well as specific internal representation of matrices (sparse triangular blocks, sparse rectangular blocks and hybrid rectangular blocks). The efficiency of the new software is demonstrated by showing computational results fr well known benchmarks as well as some crypto-challenges. For instance, for a medium size problem such as Katsura 15, it takes 849.7 sec on a PC with 8 cores to compute a DRL Gröbner basis modulo $p < 2^{16}$; this is 88 faster than Magma (V2-16-1).