The value of the determinant $\left|\begin{array}{ccc}66 & 18 & 36 \\ 1 & 3 & 4 \\ 11 & 3 & 6\end{array}\right|$ is:

0

The correct answer is Option (3) → 0

$d=\left|\begin{array}{ccc}66 & 18 & 36 \\ 1 & 3 & 4 \\ 11 & 3 & 6\end{array}\right|=6\left|\begin{array}{ccc}11 & 3& 6\\ 1 & 3 & 4 \\ 11 & 3 & 6\end{array}\right|$

Notice that the first row is 6 times the third row:

66 = 6 × 11
18 = 6 × 3
36 = 6 × 6

According to the property of determinants, if two rows are proportional, then the determinant is always equal to 0.

$∴d=0$