I've done the problem but I just want to know if I'm on the right track because I've solved many others this way. In other words, is my answer correct?

Determine for which values of $\displaystyle c$ the following matrix is invertible :

$\displaystyle \left[ \begin{array}{ccc} 1 & c & -1 \\ c & 1 & 1 \\ 0 & 1 & c\end{array} \right]$.

From my memory I think that this holds : A matrix $\displaystyle A$ is invertible if and only if its determinant is different from $\displaystyle 0$. So I calculated the determinant of the matrix above to be $\displaystyle -1-c^3$, from which I concluded that the matrix is invertible $\displaystyle \forall c \in \mathbb{C}$ such that $\displaystyle c\neq -1$.