Answer
\[x = \pm 2\]
Work Step by Step
\[\begin{gathered}
\left| {\begin{array}{*{20}{c}}
0&x \\
x&0
\end{array}} \right| = - 4 \hfill \\
{\text{Evaluate the determinant, recall that}} \hfill \\
\left| {\begin{array}{*{20}{c}}
a&b \\
c&d
\end{array}} \right| = ad - bc \hfill \\
{\text{Then,}} \hfill \\
\left| {\begin{array}{*{20}{c}}
0&x \\
x&0
\end{array}} \right| = - 4 \hfill \\
\left( 0 \right)\left( 0 \right) - \left( x \right)\left( x \right) = - 4 \hfill \\
- {x^2} = - 4 \hfill \\
{x^2} = 4 \hfill \\
{\text{Solve the equation}} \hfill \\
x = \pm 2 \hfill \\
\end{gathered} \]
