Answer
-12
Work Step by Step
Let \[A=\left|\begin{array}{ccccc} 9&1&9&9&9\\
9&0&9&9&2\\
4&0&0&5&0\\
9&0&3&9&0\\
6&0&0&7&0\end{array}\right|\]
Expanding determinant $A$ along 2nd column
\[A=(-1)^{1+2}
\left|\begin{array}{cccc} 9&9&9&2\\
4&0&5&0\\
9&3&9&0\\
6&0&7&0\end{array}\right|\]
\[A=(-1)
\left|\begin{array}{cccc} 9&9&9&2\\
4&0&5&0\\
9&3&9&0\\
6&0&7&0\end{array}\right|\]
Again expanding along 4th column
\[A=(-1)(-1)^{1+4}(2)\left|\begin{array}{ccc}
4&0&5\\
9&3&9\\
6&0&7\end{array}\right|\]
\[A=(2)\left|\begin{array}{ccc}
4&0&5\\
9&3&9\\
6&0&7\end{array}\right|\]
Again expanding along 2nd column
\[A=2[3(28-30)]\]
\[\Rightarrow A=-12\]
