Modular Matrix Inverse in Zn

Residue Matrices
Cryptography uses residue matrices: matrices in all elements are in Zn. All operations
on residue matrices are performed the same as for the integer matrices except that
the operations are done in modular arithmetic. One interesting result is that a residue
matrix has a multiplicative inverse if the determinant of the matrix has a multiplicative
inverse in Zn. In other words, a residue matrix has a multiplicative inverse if gcd
(det(A), n) = 1.