Well if we have no other information about the matrices, you could try deep learning. However if you know something about them, like they're images of either red flowers or blue flowers, then you could use traditional methods to measure those attributes, like is the matrix more red than blue, or more blue than red. Is there a spatial dependence among the elements? Why are the elements in a 2-D matrix rather than a 1-D vector? What distinguishes A from B? Can you simply look at the mean value? Or is it more complicated than that? You need to supply more context and show some small matrices as examples.