Final answer:
If matrix A is row equivalent to matrix B, then matrix B is also row equivalent to A because row operations are reversible, allowing one to transform B back into A through a series of inverse operations.
Step-by-step explanation:
To prove that if matrix A is row equivalent to matrix B, then matrix B is also row equivalent to matrix A, we need to understand the concept of row operations. To say that matrix A is row equivalent to matrix B means there exists a finite series of elementary row operations that transforms A into B. Row operations are reversible; for each row operation used to go from A to B, there is an inverse operation that can go from B to A. So when we reverse each of these operations in the opposite direction, we get a series of row operations that transform B back into A. Therefore, if A is row equivalent to B, then B must also be row equivalent to A, proving the relationship is symmetric.