Question

for a strict triangular form, does it has to be in I matrice or just the main diagonal entries are all 1]\

Answer 1

A strict triangular form is a special case of row echelon form that applies to n-equations in n-variables. There is no mention that the diagonal has to be one's.

See also:
http://www.math.tamu.edu/~yvorobet/MATH304-503/Lect1-04web.pdf
page 13.