Originally Posted by

**MathBlaster47** I'm not too sure what to do with this determinant, the question asks me to "solve the following equation.", but I don't understand what to do in order to achieve that.

$\displaystyle \begin{array}{|ccc|}0&0&-1\\3&x&0\\2&0&3\end{array}=x^2$

Do I just evaluate the determinant and work from there?

Would $\displaystyle (0\cdot x\cdot 3)+(2\cdot 0\cdot 0)+(3\cdot -1\cdot 0)-(2\cdot x\cdot -1)-(0\cdot 0\cdot 0)-(3\cdot 3\cdot 0)\rightarrow 0+0+0-(-2)x-0-0=-2x$ be a correct working for the question?

Would that mean that $\displaystyle x^2=-2x\therefore x=\{0,-2\}$?