Gauss-Jacques algorithm gets the modular inverse of a matrix. This algorithm does not use neither determinants nor the adjoint matrix and is very useful for matrices of any size.

Example:

n = 10; % size of the matrix
K = randi(100,n,n); % generate a randon matrix with size 'n'
m = 89; % the module must be a prime number
[InvMod, I] = gauss_jacques(K, m);

References:

https://www.uaq.mx/investigacion/revista_ciencia@uaq/ArchivosPDF/v11-n1/art14_numerada-VF.pdf
https://savannah.gnu.org/patch/?9691
https://www.npmjs.com/package/gauss-jacques