Solution RREF.T10 Robert Beezer

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 $\alpha$ to be nonzero makes the second operation reversible. \begin{align*} \rowopswap{i}{j}&\quad\quad\rowopswap{i}{j}\\ \rowopmult{\alpha}{i},\,\alpha\neq 0&\quad\quad\rowopmult{\frac{1}{\alpha}}{i}\\ \rowopadd{\alpha}{i}{j}&\quad\quad\rowopadd{-\alpha}{i}{j} \end{align*}