Hi !
I found very good book "First course in linear algebra"
it is free, frequently updated to weed out mistakes.
A First Course in Linear Algebra (A Free Textbook)
and here is direct link to pdf copy http://linear.ups.edu/download/fcla-oneUS-2.11.pdf
On page 32 starts "Reduced Row-Echelon Form is Unique" proof, and I am getting stuck on page 34, how they got scalar equal to zero (it is second part of Second Step) ??