This question already has an answer here:
Given $N \times M$ binary matrices (matrix containing only $0$'s and $1$'s), two matrices are called identical if one can be converted into the other by first permuting the $N$ rows and then permuting the $M$ columns of the resulting matrix. Find the number of non-identical matrices.
I'm not really sure of how to begin this problem either. It's some recursion (or composition of more than one recursion) and I can't figure that out. May I get some valid hints?