Prove that the determinant is a multiple of $17$ without developing it Let, matrix is given as :
$$D=\begin{bmatrix}
1 & 1 & 9 \\
1 & 8 & 7 \\
1 & 5 & 3\end{bmatrix}$$

Prove that the determinant is a multiple of $17$ without developing it?


I saw a resolution by the Jacobi method , but could not apply the methodology in this example.

$$
|D|
=
\begin{vmatrix}
1 & 1 & 9 \\
1 & 8 & 7 \\
1 & 5 & 3\end{vmatrix}
=
\begin{vmatrix}
1 & 1 & 9 \\
0 & 7 & -2 \\
0 & 4 & -6\end{vmatrix}
=
\begin{vmatrix}
1 & 1 & 9 \\
0 & 7 & -2 \\
0 & 0 & -\dfrac{34}{7}\end{vmatrix}
=
1 \times 7 \times -\dfrac{34}{7}
=
-34
=-2 \times 17
$$
