Row echelon form is indeed an upper triangular matrix, characterized by zeros below the main diagonal. The determinant of a matrix in row echelon form can be either 1 or 0, depending on the values on the diagonal, which do not need to be 1s. Row operations can alter the determinant; multiplying a row changes the determinant by that factor, while swapping rows multiplies it by -1, and adding a multiple of one row to another does not affect the determinant. The discussion highlights the relationship between row echelon form and determinants, emphasizing the impact of row operations. Understanding these concepts is essential for matrix analysis and linear algebra.