Answer
\[x = \pm 3\]
Work Step by Step
\[\begin{gathered}
\left| {\begin{array}{*{20}{c}}
x&0 \\
0&x
\end{array}} \right| = 9 \hfill \\
{\text{Evaluate the determinant, recall that}} \hfill \\
\left| {\begin{array}{*{20}{c}}
a&b \\
c&d
\end{array}} \right| = ad - bc \hfill \\
{\text{Then,}} \hfill \\
{x^2} - 0 = 9 \hfill \\
{x^2} = 9 \hfill \\
{\text{Solve the equation}} \hfill \\
x = \pm 3 \hfill \\
\end{gathered} \]
