Generic linear algebra echelon form question

[dmitriylm]

Homework Statement

What is the reduced echelon form of a n x n nonsingular matrix? Briefly explain.

Homework Equations

The Attempt at a Solution

I know that a n x n nonsingular matrix will always result in echelon form will always have a diagonal orientation with a single digit in its own row.

For example:
A 2x2 matrix in echelon form will appear as

1 0
0 1

A 3x3 matrix in echelon form will appear as

100
010
001

etc.

Is there a specific (more elegant) way that this behavior would be described?

 

[Char. Limit]

Those all look like an n-dimensional identity matrix to me.