Identifying matrices as REF, RREF, or neither

[crememars]

TL;DR Summary: we are given a set of coefficient matrices (shown below) and we need to determine whether they are in REF, RREF, or neither.

Hello! I am having a lot of trouble identifying these matrices, and using the criteria checklist is not helping very much. Here is what I am working with:

Matrix A =
0 0 1
0 0 0
0 0 0

*I think this would be RREF. It has a leading 1 with no non-zero entries above or below it. The two zero rows are confusing me a little though.

Matrix B =
0 0
0 0
0 0

*This one has no leading entries at all, so does it automatically classify as neither REF nor RREF?

Matrix C =
0 0 1

*This matrix has only one row. We did not learn much about exceptions in class, but I feel as if matrices consist of at least more than two equations. Therefore, this matrix should be in neither form. If my reasoning is wrong, then I think that this might be RREF, since there is a leading 1 with no non-zero entries below or above it.

I would sincerely appreciate any help with these problems. Thank you!

 

[Mark44]

*This matrix has only one row. We did not learn much about exceptions in class, but I feel as if matrices consist of at least more than two equations.

A matrix can have as few as one row or as few as one column. A matrix can represent a system of one or more equations, but it does not consist of equations.

How does your book define the terms REF (row-echelon form) and RREF (reduced row-echelon form)?
Since all three matrices you showed can't be simplified further, I would say that all three are RREF.