Is it true that is just the set of all matrices over the field And is the kernel (the set of all vectors in the domain that get mapped to the zero vector in the range), and is the range of Because, if all of this is true, your problem is a trick question. It's impossible to answer, because the kernel is a subset of whereas the range is a subset of I suppose you could think of the equals sign as a sort of embedding, but that's not very usual.