Hey I think i got it. 

Thx. the problem to me was that the 'e' was  not sorted. So I did sort them and got the result. I can see you just end the calculation with a prove. I do see it now. Now I just need to work with it. 

I only need the final answer.

I don't get it work. I have tried to figure this out over the night and some days now. 

I have tests your answers in Maple T.A. Maybe I just don't do it right.

Pagan, with you I get the original matrix A. If I answer that, I get it wrong. And robert, here I get solution with many unknown factors, and its not a matrix. 

I will try to post the Maple TA questions, and I copy a google translate here:

"There has been a diagonaliserbar matrix

A=

(-3 0 0)

(0 -3 0)

(22 6 -1)

Answer

the following two questions.

(I)Determine own value to A.

The answer must be given as numbers separated by commas. Whose own values are, 1, -1, 2and must answer is given as 1 -1.2 If the eigenvalue with multiplicity 2, and the third eigenvalue is -4 to be the answer given by-4,1,1So repetition corresponding to multiplicity. The order does not matter.

Your Answer: -3, -3, -1

Comment: Own values are -3, -3, -1

(Ii)Sort the found eigenvalues by size, and let D denote the 3x3 diagonal matrix having the smallest eigenvalue as the entry D₁₁ and the largest as input D₃₃.

Define an 3x3 invertible matrix P, so that A=PDP.

The answer must be in Maple syntax for a matrix, for example, enter the matrix

(1 2 3)

(0 5 5)

(0 0 6)

as

Matrix ([[1,2,3], [0,4,5], [0,0,6]])

Be careful that you do not swap for the rows and columns. Use the preview feature to see that you have typed what you meant to type.
Your Answer: Matrix ([[-3,0,0], [0, -3.0], [22.6, -1]])

Comment:A possible correct answer is
There are many other correct answers.

P=

(1 0 0)

(-3 1 0)

(-2 -3 1)

"