Multiple neural networks or multiple outputs?
You can do either.

If the learning tasks are related at all (i.e., the meaning of the columns of B are related), it's probably better to have one neural network with multiple outputs.  This is often more effective, because the first few stages of that neural network might do some processing that is relevant to all of the outputs -- e.g., it might look for some local patterns or properties of the input that can then be useful for predicting all of the outputs.  The network might take a bit longer to train if you use one big network rather than many smaller networks, but usually this is worth it if it leads to better accuracy.

But if you're not sure, you can always try both approaches and see which works better.