# Talk:Elementary Row Operations as Matrix Multiplications

No, it would not hold. Take $\mathbf A = \left[ \begin{array}{ccc} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{array}\right], \; \mathbf E = \left[ \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 1 \end{array}\right]. \; \mathbf E$ is an elementary matrix, then using the conventional matrix multiplication:
$\mathbf {AE} = \left[ \begin{array}{ccc} 1 & 2 & 1 \\ 1 & 2 & 1 \\ 1 & 2 & 1 \end{array}\right]$ which is an elementary column operation on A. --HumblePi (talk) 13:08, 3 December 2016 (EST)