Given, If $A=\left[\begin{array}{cccc}\sqrt{2020}& \sqrt{2021}& \sqrt{2021}& \sqrt{2023}\\ \sqrt{4040}& \sqrt{4042}& \sqrt{4044}& \sqrt{4046}\\ \sqrt{6060}& \sqrt{6063}& \sqrt{6066}& \sqrt{6069}\\ \sqrt{8080}& \sqrt{8084}& \sqrt{8088}& \sqrt{8092}\end{array}\right]$ 

$A=\left[\begin{array}{cccc}\sqrt{2020}& \sqrt{2021}& \sqrt{2022}& \sqrt{2023}\\ \sqrt{2}\sqrt{2020}& \sqrt{2} \sqrt{2021}& \sqrt{2}\sqrt{2022}& \sqrt{2}\sqrt{2023}\\ \sqrt{3}\sqrt{2020}& \sqrt{3}\sqrt{2021}& \sqrt{3}\sqrt{2022}& \sqrt{3}\sqrt{2023}\\ 2\sqrt{2020}& 2\sqrt{2021}& 2\sqrt{2022}& 2\sqrt{2023}\end{array}\right]$

$R_4\to R_4-2R_1 \& R_3\to R_3-\sqrt{3}{R}_1$

$A=\left[\begin{array}{cccc}\sqrt{2020}& \sqrt{2021}& \sqrt{2022}& \sqrt{2023}\\ \sqrt{2}\sqrt{2020}& \sqrt{2} \sqrt{2021}& \sqrt{2}\sqrt{2022}& \sqrt{2}\sqrt{2023}\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right]$

$R_2\to R_2-\sqrt{2}{R}_1$

$A=\left[\begin{array}{cccc}\sqrt{2020}& \sqrt{2021}& \sqrt{2022}& \sqrt{2023}\\ 0& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right]$

Hence, the rank of the matrix $A$ is $1$.