math111_logo Row Operation


Exercise Prove that if a matrix A can be changed to a matrix B by row operations, then the matrix B can also be changed to a matrix A by row operations.

Answer If applying r[row i] + [row j] to A gives us B, then applying (-r)[row i] + [row j] to B gives us A back.

If applying [row i] ↔ [row j] to A gives us B, then applying the same operations again to B gives us A back.

If applying d[row i] to A gives us B, then applying d-1[row i] to B gives us A back.