> how to calculate matrix inverse 100 x 100...
Short answer: you don't.
Longer answer: instead of calculating an explicit (numerically very
unstable) inverse of a matrix A you calculate PA= LU where P is a
row permutation matrix, L and U are lower and upper triangular
matrixes respectively and L has just 1s on its main diagonal.
Google for LUP decomposition.
kind regards,
Jos