Given the matrix $\displaystyle \begin{pmatrix} 1 & 2 & -1\\ 1 & 0 & 1 \\ 4 & -4 & 5 \end{pmatrix}$, I've to find a vector x, such that Ax = x.

I'm not quite sure what's the best way of solving a question like this, I can try some values that could be correct, doing some half educated guesses, but that just seems clumsy and slow. Any tips?