'Operations' is mathematician-ese for 'procedures'. The four 'basic operations' on numbers are addition, subtraction, multiplication, and division. For matrices, there are three basic row operations; that is, there are three procedures that you can do with the rows of a matrix. Elementary row operation σ is obtained by applying σ to the identity matrix. In particular, this implies that E σ is unique. Theorem Any elementary row operation σ 1 can be undone by applying another elementary row operation σ 2. Moreover, the operation σ 1 will undo the operation σ 2. Corollary Elementary matrices are invertible.