Question 385727
Yes. Every row operation corresponds with an elementary matrix (i.e., a matrix formed by applying the same row operation on the identity matrix once) that you right-multiply with the given matrix. This elementary matrix is always nonsingular , and thus has an inverse.  Hence we can just right-multiply the end matrix with the inverses of these elementary matrices (which again corresponds to a sequence of row operations), and get back to the original given matrix.