Question

Given that the determinant of the matrix $\left[\begin{array}{ccc}1& 3& 0\\ 2& 6& 4\\ -1& 0& 2\end{array}\right]$ is $-12$. The determinant of the matrix $\left[\begin{array}{ccc}2& 6& 0\\ 4& 12& 8\\ -2& 0& 4\end{array}\right]$ is

• A. $-96$
• B. $-24$
• C. $24$
• D. $96$

Answer 1

The correct option is A $-96$

Let $A=\left|\begin{array}{ccc}1& 3& 0\\ 2& 6& 4\\ -1& 0& 2\end{array}\right|=-12$
$\left|\begin{array}{ccc}2& 6& 0\\ 4& 12& 8\\ -2& 0& 4\end{array}\right|=2^3\left|A\right|$
$=8\times -12=-96$