Maybe you would like to use 'echelon' instead of 'triangularize'
(%i1) A:matrix([0,1,2],[-1,0,3],[-2,-3,0]);
(%o1) matrix([0,1,2],[-1,0,3],[-2,-3,0])
(%i2) echelon(%);
(%o2) matrix([1,0,-3],[0,1,2],[0,0,0])
The user documentation for 'triangularize' should be changed
from "Returns the upper triangular form of the matrix `M'. " to
"Returns an upper triangular form of the matrix `M'."
Barton