Question

Consider the matrices $A,B,C$ and $D$ with order $2\times 4,4\times 3,3\times 3$ and $3\times 2$ respectively. Let $M={\left(2AB{C}^{2020}D\right)}^6$ and $\left|M\right|=\lambda {\left|AB{C}^{2020}D\right|}^6$ , then $\lambda$ is equal to

• A. $1024$
• B. $4096$
• C. $64$
• D. $4$

Answer 1

Answer: (B)

$M={\left(2AB{C}^{2020}D\right)}^6$ (Given)
$\left|M\right|={\left|2AB{C}^{2020}D\right|}^6$
$\because AB{C}^{2020}D$ is a $2\times 2$ matrix
Hence, $\left|2AB{C}^{2020}D\right|=2^2\left|AB{C}^{2020}D\right|$
Therefore,
$\left|M\right|=4^6{\left|AB{C}^{2020}D\right|}^6$
$\Rightarrow \lambda =4096$