Yes it is possible! You probably did not fix it, because it is in the chapter "Linear Algebra" and not "Matrices".
In GSL, you first compute the LU decomposition, and then use it to determine the opposite through
int gsl_linalg_LU_invert (const gsl_matrix * LU, const gsl_permutation * p, gsl_matrix * reverse)
See here for a detailed example https://lists.gnu.org/archive/html/help-gsl/2008-11/msg00001.html
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