Output Matrix in relation to category
It's tempting to use the Matrix block for things that might actually be better as a a channel or a structure.  I thing this might be the case here.

The way you've set it up is fine, relating each FAQ to a category is a good approach.

In any event, the plugin groupBy should help you:

https://github.com/timkelty/groupby-craft

Or you can look at this example:

http://craftcookbook.net/recipes/279