## Divisibility of a determinant

Numbers 697, 476 and 969 are divisible by 17. Prove that 17 divides the determinant of the following matrix $$\begin{pmatrix} 6 & 9 & 7\\ 4 & 7 & 6\\ 9 & 6 & 9\\ \end{pmatrix}$$ without calculating it.
Formally: $$\begin{vmatrix} 6 & 9 & 7\\ 4 & 7 & 6\\ 9 & 6 & 9\\ \end{vmatrix} = \begin{vmatrix} 6 & 9 & 697\\ 4 & 7 & 476\\ 9 & 6 & 969\\ \end{vmatrix} = 17\cdot \begin{vmatrix} 6 & 9 & \frac{697}{17}\\[1ex] 4 & 7 & \frac{476}{17}\\[1ex] 9 & 6 & \frac{969}{17}\\ \end{vmatrix}$$