\[\begin{array}{l}
\frac{a}{b} = \frac{3}{b} = \frac{b}{a}\,\,\left( {a,\,b \ne 0} \right) \Rightarrow \left\{ \begin{array}{l}
ab = 3b\\
{b^2} = 3a
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
a = \frac{{{b^2}}}{3}\\
\frac{{{b^2}}}{3}.b = 3b
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
a = \frac{{{b^2}}}{3}\\
{b^2} = 9
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
a = \frac{{{b^2}}}{3}\\
\left[ \begin{array}{l}
b = 3\\
b = - 3
\end{array} \right.
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
a = \frac{9}{3} = 3\\
\left[ \begin{array}{l}
b = 3\\
b = - 3
\end{array} \right.
\end{array} \right. \Leftrightarrow b = a = 3.
\end{array}\]
