Answer
$54.$
Work Step by Step
Since we have $$\left[\begin{array}{rrr} {-3} & {6}&{9} \\ {6} & {9}&{12}\\{9}&{12}&{15}\end{array}\right]=3\left[\begin{array}{rrr} {-1} & {2}&{3} \\ {2} & {3}&{4}\\{3}&{4}&{5}\end{array}\right]=3\left[\begin{array}{rrr} {-1} & {2}&{3} \\ {0} & {7}&{10}\\{0}&{10}&{14}\end{array}\right]$$
then, we get
$$\left|\begin{array}{rrr} {-3} & {6}&{9} \\ {6} & {9}&{12}\\{9}&{12}&{15}\end{array}\right|=3^3\left|\begin{array}{rrr}{-1} & {2}&{3} \\ {0} & {7}&{10}\\{0}&{10}&{14}\end{array}\right|=27(-1)(98-100)=54.$$
