# How to show that eigenvalues of AB and BA are same?

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.

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