characteristic polynomial

$\displaystyle The \emph{characteristic polynomial} $\chi(\lambda)$ of the$

$\displaystyle $3 \times 3$~matrix$

$\displaystyle \[ \left( \begin{array}{ccc}

2 & 1 & 0 \\

0 & 3 & 0 \\

1 & 0 & 0\end{array} \right)\]

$

is given by the formula

$\displaystyle \[ \chi(\lambda) = \left| \begin{array}{ccc}

\lambda - 2 & -1 & 0 \\

0 & \lambda - 3 & 0 \\

-1 & 0 & \lambda \end{array} \right|.\]

$

Characteristic polynomial should be x^3-5*x^2+6*x but cannot make the metrix satisfy the equation.

Can someone please help me.

Thanks