Question

Let $A^{-1}\left[\begin{array}{ccc}1& 2017& 2\\ 1& 2017& 4\\ 1& 2018& 8\end{array}\right]$. Then $|2A|-|2A^{-1}|$ is equal to.

• A. $3$
• B. $-3$
• C. $12$
• D. $-12$

Answer 1

The correct option is C $12$

$\left|A^{-1}\right|=\frac{1}{\left|A\right|}$

given matrix $A^{-1}=$

$$\left[\begin{array}{ccc}1& 2017& 2\\ 1& 2017& 4\\ 1& 2018& 8\end{array}\right]$$

solving the determinant

$\left|A^{-1}\right|=\frac{1}{\left|A\right|}=-2$

$\left|kA\right|=k^n\left|A\right|$

where n is the order of the matrix

$-\left|2A^{-1}\right|+\left|2A\right|$

$=-(-2)\times 2^3+\frac{-1}{2}\times 2^3=12$