Is it always possible using the elementary row operations for matrices to transform......?

Question

any square matrix into echelon form with all 1's along its main diagonal?

Answer 1

No. Try to transform the 1×1 matrix [0] into echeclon form with all 1s along the main diagonal. If that example seems too trivial, consider the matrix:

[1, 2, 3]
[2, 4, 3]
[3, 6, 3]

The reduced-row echelon form of this matrix is:

[1, 2, 0]
[0, 0, 1]
[0, 0, 0]

Note that two of the three elements on the main diagonal are zeros. In general, the echelon form of a square matix will have all 1s along the main diagonal if and only if the matrix is invertible - i.e. its determinant is nonzero.

Answer 2

Not if one row is a multiple of another.

Example:

2 4 5
4 8 10
3 3 1