Thread: Linear alg. question concerning elementary row operations

Hi I have to prove this statement:
Prove that if a matrix Q can be obtained from a matrix P by an elementary row operation, then P can be obtained from Q by an elementary matrix of the same type.
What would the proof of this look like?
Thanks

Originally Posted by dannyboycurtis

Hi I have to prove this statement:
Prove that if a matrix Q can be obtained from a matrix P by an elementary row operation, then P can be obtained from Q by an elementary matrix of the same type.
What would the proof of this look like?
Thanks

Hi - Outlines of the prove
1. Note/Show - Inverse of every type of row operation is also a row operation
2. Use induction over number of row operations,n, needed for P->Q. Prove for the base case where n=1. You have to show that inverse of all three types of row operations restore the matrix to the original form.
3. Once this is done just use the induction logic to complete the prove.

I would assume this is a std way and can be found in most of the textbooks.
Thanks