Let $A$ be an $m\times n$ matrix and $B$ be an $n\times m$ matrix. How to use Jordan canonical form to prove the matrix shown below are similar. Given matrices are $$\begin{bmatrix} AB&0\\ B&0\end{bmatrix}$$ and $$\begin{bmatrix} 0&0\\ B&BA\end{bmatrix}$$ How to find their Jordan forms? I have no idea.

  • $\begingroup$ No need to use any Jordan form. See, e.g., here. $\endgroup$ – Algebraic Pavel Nov 23 '18 at 15:21

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