Prove that each of the three row operations (Definition RO) is reversible. More precisely, if the matrix B is obtained from A by application of a single row operation, show that there is a single row operation that will transform B back into A

If we can reverse each row operation individually, then we can reverse a sequence of row operations.

The operations that reverse each operation are listed below, using our shorthand notation.

Notice how requiring the scalar α to be non-zero makes the second operation reversible.