given a matrix $B$
for example
$$ B= \begin{pmatrix} 1 & 1 & 1 \\ 2 & 2 & 5 \\ 4 & 6 & 8 \\ \end{pmatrix} $$ I know how to perform the Gaussian elimination w/wo pivoting but I just wanted to know when is it possible to complete the algorithm of elimnation without pivoting till the end cuz I'm coding a program doing that and I want to add a condition in it to make sure that it works correctly