Non linear state equation show that nominal output is 1

Question

Do you help me with this?

Consider the nonlinear state equation

$\dot{x} = \begin{bmatrix} u \\ u x_1 -x_3 \\ x_2 - 2x_3 \end{bmatrix}$

$y = x_2 - 2x_3$

with nominal initial state $x^* = \begin{bmatrix} 0 & -3 & 2 \end{bmatrix}^T$ and constant nominal input $u^* = 1$. Show that the nominal output is $y^* = 1$

I tried this... but I'm sure is incorrect!!! I don't know why helas.

$y= -3- (-4) = 1$

or maybe:

$y^* = C[e^{At}x^* + e^{At}(A^{-1}- I)e^{At}]$?