SOLUTION: if matrix B results from a matrix A by applying elementary row operation, is there always an elementary row operation that cna be applied to B to recover A?

Question 385727: if matrix B results from a matrix A by applying elementary row operation, is there always an elementary row operation that cna be applied to B to recover A?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
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.
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