Question

If $A_n=\left[\begin{array}{cc}1-n& n\\ n& 1-n\end{array}\right]$ then $\left|A_1\right|+\left|A_2\right|+\dots +\left|A_{2021}\right|=$

• A. $-2021$
• B. $(2021{)}^2$
• C. $-(2021{)}^2$
• D. $4042$

Answer 1

Answer: (C)

$A_n=\left[\begin{array}{cc}1-n& n\\ n& 1-n\end{array}\right]$
$\left|A_n\right|=(1-n{)}^2-n^2$
$=1+n^2-2n-n^2$