# Transition matrix of a specific matrix

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?