Let $A$ be the square matrix of order 3 , then $|kA|$, where $k$ is a scalar, is equal to:

$k^3|A|$

let $A=\left[\begin{array}{lll}a_1 & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_3 & a_{32} & a_{33}\end{array}\right]$

$|A|=\left|\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right|$

so $k A=\left[\begin{array}{lll}k a_{11} & k a_{12} & k a_{13} \\ k a_{21} & k a_{22} & k a_{23} \\ k a_{31} & k a_{32} & k a_{33}\end{array}\right]$

$\Rightarrow |k A|=\left|\begin{array}{lllll}k a_{11} & k a_{12} & k & a_{13} \\ k a_{21} & k a_{22} & k & a_{23} \\ k a_{31} & k a_{32} & k & a_{33}\end{array}\right| = k . k . k \left|\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right|$

$|k A|=k^3|A|$