Recently, I learned that for each matrix, there are several row echelon forms, and a singular reduced row echelon form that each matrix can be reduced down to.
However, the conditions under which a matrix can be deemed reduced to RREF or REF seem really convoluted and complicated.
I'll focus on RREF for this question --
Pivots are $1$, are the leftmost nonzero in their row, are the only nonzero in their column? And then all rows full of zeros are on the bottom? And the matrix should be upper triangular? Am I missing anything, and is their some sort of pneumonic, trick, or picture in mind I should have when reducing?