Non-Singular matrix - RREF proof

[Soupy11]

Homework Statement

Prove that the only n x n non-singular reduced row echelon matrix is I sub n.

The Attempt at a Solution

Not even remotely sure where to start here - the statement looks similar to the definition of a non-singular matrix. Yet there is something subtly different and I am having an issue grasping it. I see in the next chapter there are some tools explored using elementary matrices, but this specific question is before that material so I am assuming that the proof must be done without that knowledge.

If A is a nxn matrix not equal to I yet non-singular

There exists a matrix X that satisfies
AX=I

 

[silvermane]

Homework Statement

Prove that the only n x n non-singular reduced row echelon matrix is I sub n.

The Attempt at a Solution

Not even remotely sure where to start here - the statement looks similar to the definition of a non-singular matrix. Yet there is something subtly different and I am having an issue grasping it. I see in the next chapter there are some tools explored using elementary matrices, but this specific question is before that material so I am assuming that the proof must be done without that knowledge.

If A is a nxn matrix not equal to I yet non-singular

There exists a matrix X that satisfies
AX=I

Well, if it is non-singular doesn't that mean you won't loose a pivot when you simplify? Thus what would this mean if we simplified all the way?

 

[fzero]

You probably want to start with the definition of row echelon matrix and reduced row echelon matrix.