Is Matrix A Similar to Its Row Echelon Form?

[Nope]

Homework Statement

just wondering if A is similar to the reduced(or non-reduced) row echelon form of A

Homework Equations

The Attempt at a Solution

 

[lanedance]

not in general

similar matricies have the same eigenvalues

row operations, with the exception of row addition lead to changes in the eigenvalues and so the determinant of the matrix they are applied to
http://en.wikipedia.org/wiki/Elementary_matrix