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Let $ A = \begin{bmatrix} 3&3&3 \\ 3&3&3\\ 3&3&3\\ \end{bmatrix} $

I know that its rational canonical form is

$ \begin{bmatrix} 0&0&0 \\ 0&0&0\\ 0&1&9\\ \end{bmatrix}$

Since its characteristic polynomial is p(x) = - x²(x-9) and minimal polynomial m(x) = x(x-9)

Can you provide a transition matrix X in M(3,Z) with determinant +/- 1 using the row operation from the invariant factor decomposition?

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