Inverse matrices computed with minors are very bad news for matrix sizes more than say 2 or 3.
Inverse matrices are usually bad news anyway. They waste operations, storage, and tend to decrease numerical accuracy. This is especially so for sparse matrices.
If you really need the inverse matrix, augment the matrix to be inverted with the unit matrix and reduce to row-canonical form. The inverse matrix will then be in the right hand side.
Partial pivoting may be used as needed.