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  4. If An=[1-n n n 1-n] then |A1|+|A2|+ ldots+|A2021|=

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Q. If $A_{n}=\begin{bmatrix}1-n & n \\ n & 1-n\end{bmatrix}$ then $\left|A_{1}\right|+\left|A_{2}\right|+\ldots+\left|A_{2021}\right|=$

KCETKCET 2022Determinants

Solution:

$A_{n}=\begin{bmatrix}1-n & n \\ n & 1-n\end{bmatrix}$
$\left|A_{n}\right|=(1-n)^{2}-n^{2}$
$=1+ n ^{2}-2 n - n ^{2}$