Q8

MCQ1 mark, −0.33

Let

A=\left[\begin{array}{llll} 1 & 2 & 3 & 4 \\ 4 & 1 & 2 & 3 \\ 3 & 4 & 1 & 2 \\ 2 & 3 & 4 & 1 \end{array}\right]

and

B=\left[\begin{array}{llll} 3 & 4 & 1 & 2 \\ 4 & 1 & 2 & 3 \\ 1 & 2 & 3 & 4 \\ 2 & 3 & 4 & 1 \end{array}\right]

Let $\operatorname{det}(A)$ and $\operatorname{det}(B)$ denote the determinants of the matrices $A$ and $B,$ respectively. Which one of the options given below is $\text{TRUE}?$

(A)

$\operatorname{det}(A)=\operatorname{det}(B)$

(B)

$\operatorname{det}(B)=-\operatorname{det}(A)$

(C)

$\operatorname{det}(A)=0$

(D)

$\operatorname{det}(A B)=\operatorname{det}(A)+\operatorname{det}(B)$

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