For most of these you’d likely be able to understand the concept at a good enough level to see the contradiction if you looked up the definition of the concepts

For most of these you’d likely be able to understand the concept at a good enough level to see the contradiction if you looked up the definition of the concepts. For example I think the one about tr(AB)=tr(BA) not holding for arbitrary permutations across a set of more than two matrices is something you could try proving yourself.