given the Crank-Nicolson method for $f:(t,z)\mapsto az$
$$ \begin{equation}\text{given } z^0 \\ z^{n+1}=z^n+\frac{\Delta t}{2}f(t^n,z^n)+\frac{\Delta t}{2}f(t^{n+1},z^{n+1}) \end{equation}$$
I want to show that the method is defined if, and only if $a \leq 0$. Any idea?