Proof concerning eigen values

Question

Could somebody help me into proving this theorem?

if $A$ and $B^{H}$ are in $C^{m\times n}$ with $m\geq n$, then $\lambda (AB) = \lambda(BA) \cup \lbrace 0, \ldots ,0\rbrace.$

Thenks, Elnaz

Answer 1

Hint: $AB x = ax\implies BA(Bx) = aBx$

$BA y = ay\implies AB(Ay) = aAy$