for a strict triangular form, does it has to be in I matrice or just the main diagonal entries are all 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.
To determine whether a matrix is in strict triangular form, we need to check whether it is an upper triangular or a lower triangular matrix where all the elements on the main diagonal are zero.
An upper triangular matrix is a matrix where all elements below the main diagonal (i.e., elements with row indices greater than column indices) are zero. Similarly, a lower triangular matrix is a matrix where all elements above the main diagonal (i.e., elements with row indices less than column indices) are zero.
In the case of a strict triangular matrix, not only do all the off-diagonal elements need to be zero, but the main diagonal elements must also be zero (instead of one in the case of an identity matrix).
Therefore, a strict triangular matrix does not have to be an identity matrix. The requirement is that all the elements on the main diagonal are zero, and all the off-diagonal elements are zero as well, depending on whether it is an upper triangular or lower triangular matrix.