Answer
\[54\]
Work Step by Step
\[\begin{gathered}
{\text{Use the Determinant Theorem 7}}{\text{.}}\,\,\left( {{\text{See page 880}}} \right) \hfill \\
{\text{If matrix }}A{\text{ is in triangular form}},{\text{ having only zeros either above or }} \hfill \\
{\text{below the main diagonal}},{\text{ then}}\,\left| A \right|{\text{is the product of the elements on }} \hfill \\
{\text{the main diagonal of }}A.\,\,{\text{Therefore,}} \hfill \\
A = \left| {\begin{array}{*{20}{c}}
1&6&7 \\
0&6&7 \\
0&0&9
\end{array}} \right| = \left( 1 \right)\left( 6 \right)\left( 9 \right) = 54 \hfill \\
\end{gathered} \]
