Is Matrix A Similar to Its Row Echelon Form?

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Homework Statement


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


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The Attempt at a Solution

 
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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
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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