Use determinants to find which real values of c make each of the following matrices invertible So i was given this question 
Use determinants to find which real values of c make each of the following matrices invertible
$
\left[ {\begin{array}{cc}
0 & c & -c \\
-1 & 2& 1 \\
c & -c & -c
\end{array} } \right]
$
When i look at the solutions for this question they usually adding or subtracting a column or row to one another, until there is two consecutive $0s$ in the row or column then make a 2x2 matrix. I understand the logic behind finding a determinant, but for this question and similar ones is there a rule or method to go about solving these kinds of problems, and how to do it?

If a given square matrix is invertible, then determinant of it should be non zero. The determinant of this matrix is $-c(c-c)-c(c-2c)=c^2$. So, any non zero $c$ would make this matrix invertible.
