What's the inverse of a 2x4 matrix?

Mxn Matrices do not have an inverse solution for m ≠ n, so your 2x4 will not have a solution.

Generally, inverting matrices is done through finding the determinant of the square matrix and then performing an operation on the matrix based on the size of the matrix.

Wikipedia has a good article on Matrix inversion, take a look there for more information.