We have written a general purpose code for exact inversion of large matrices in C language by treating matrices in block forms. We have optimized the computation speed using in-place inversion, dynamic memory handling and recursion techniques. This code is written to adapt with programs in C and Fortran language, which requires faster and exact solution for system of linear equations. We have applied it in our study of tau neutrino events at India based Neutrino Observatory (INO). With this program the time required for computing the exact inversion of matrices of order 100, 1000 are 6ms and 5.24s respectively in Intel i7 6700 CPU, 8GB RAM machine. We also present our procedure to implement parallel processing for calculating inverse by treating the matrix as large number of blocks and performing simultaneous operations among them.