If A row B explain why the basic columns in A occupy exactly

If A row B, explain why the basic columns in A occupy exactly the same positions as the basic columns in B.

Solution

We know that if the two matrices A and B are row equivalent, then further row operations will reduce both to the same Row Reduced Echelon Form (RREF). Since the pivot positions are defined in terms of the RREF, therefore, the basic columns will be same for A and B .