Chapter 1 - Linear Equations in Linear Algebra - 1.4 Exercises - Page 42: 33

See solution

If the solution is unique, there are no free variables, which means there is a pivot in each column. This means the reduced echelon form of A is $\begin{bmatrix} 1&0&0\\ 0&1&0\\ 0&0&1\\ 0&0&0 \end{bmatrix}$. In reduced echelon form, the leading entry of each row that has a pivot is 1 and 1 is the only non zero entry in the pivot columns.