Question

If $A=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$ and $B=\sum _{r=1}^{2021}{A}^r$ then value of $\left|B\right|$ is

• A. $2021$
• B. ${2021}^2$
• C. $-2021$
• D. $0$

Answer 1

The correct option is B

${2021}^2$

Find the value of $\left|B\right|$:

Given, $A=I$, $B=I+I+I+\dots .2021$ times

$\Rightarrow$$B=2021\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

$=\left[\begin{array}{cc}2021& 0\\ 0& 2021\end{array}\right]$

$\mathbf{\therefore }\left|B\right|\mathbf{}\mathbf{=}\mathbf{}{\mathbf{2021}}^{\mathbf{2}}$

Hence, Option ‘B’ is Correct.