Linear Algebra-Uniqueness of rref

[Roni1985]

Homework Statement

"Prove a specific rref matrix is unique"

Homework Equations

The Attempt at a Solution

This is all I have on my review sheet for my next exam. I have the proof of the uniqueness of rref but how do you prove a specific rref matrix is unique ?

say that's any nonsingular matrix in R^3
Would appreciate any hints.

Thanks,
Roni.

 

[Dustinsfl]

If the system is unique, we know it is nonsingular. What does a nonsingular rref matrix look like? It is a diagonal matrix with 1s in the diagonals or identity matrix.

Also, if the nxn matrix is unique, the column vectors are linearly independent.