JEE Main 2022 · 29 Jun · Shift 2 · Mathematics Q3

← JEE Main 2022 · 29 Jun · Shift 2

MathematicsSingle correct+4 / -1Question 3 of 90

Let $A=\begin{pmatrix}2&-1\\0&2\end{pmatrix}$ . If $B=I-{}^5C_1(\operatorname{adj}A)+{}^5C_2(\operatorname{adj}A)^2-\dots-{}^5C_5(\operatorname{adj}A)^5$ , then the sum of all elements of the matrix B is

-5

-6

-7

-8

Answer and worked solution

Official answer: C

Binomial. $B=(I-\operatorname{adj}A)^5$ with $\operatorname{adj}A=\begin{pmatrix}2&1\\0&2\end{pmatrix}$ , so $I-\operatorname{adj}A=\begin{pmatrix}-1&-1\\0&-1\end{pmatrix}=-(I+N)$ , $N^2=0$ .

Power. $B=-(I+5N)=\begin{pmatrix}-1&-5\\0&-1\end{pmatrix}$ ; sum $-7$ .

(C)

Topics:Adjoint and inverse Binomial expansion

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JEE Main 2022 · 29 Jun · Shift 2, Mathematics question 3