JEE Main 2022 · 26 Jul · Shift 1 · Mathematics Q4

MathematicsSingle correct+4 / -1Question 4 of 90

Let A be a $2\times2$ matrix with $\det(A)=-1$ and $\det((A+I)(\operatorname{Adj}(A)+I))=4$ . Then the sum of the diagonal elements of A can be :

-1

-\sqrt2

Answer and worked solution

Official answer: B

Expand. $(A+I)(\operatorname{adj}A+I)=\det A\,I+A+\operatorname{adj}A+I=A+\operatorname{adj}A=(\operatorname{tr}A)I$ for $2\times2$ .

Determinant $(\operatorname{tr}A)^2=4$ : trace $\pm2$ , so 2.

(B)

Topics:Adjoint and inverse

JEE Main 2022 · 26 Jul · Shift 1, Mathematics question 4