Searching Shift/Permutation Matrix

Question

Is there a Matrix P, which does:

$$AP=A'$$ $$A=\begin{bmatrix} a_{00} & 0 & 0\\ a_{10} &a_{11} & 0\\ a_{20} &a_{21} & a_{22} \end{bmatrix}$$ $$A'=\begin{bmatrix} a_{00} & a_{11} & a_{22}\\ a_{10} & a_{21}& 0\\ a_{20} & 0 & 0 \end{bmatrix}$$

Answer 1

Yes of course, given that A is invertible we have

$$AP=A' \iff P=A^{-1}A'$$