Question

Using properties of determinants, the negative of $\left|\begin{array}{ccc}18& 40& 89\\ 40& 89& 198\\ 89& 198& 440\end{array}\right|$ would be

Answer 1

$\left|\begin{array}{ccc}18& 40& 89\\ 40& 89& 198\\ 89& 198& 440\end{array}\right|$
$C_3\to C_3-{2C}_2$
$=\left|\begin{array}{ccc}18& 40& 9\\ 40& 89& 20\\ 89& 198& 44\end{array}\right|$
$C_1\to C_1-{2C}_2$
$\left|\begin{array}{ccc}0& 40& 9\\ 0& 89& 20\\ 1& 198& 44\end{array}\right|$
$=1(800-801)=-1$
Negative of the determinant $-1$ is $1$