JEE Main 2022 · 27 Jun · Shift 2 · Mathematics Q4

MathematicsSingle correct+4 / -1Question 4 of 90

Let $A$ and $B$ be two $3\times3$ matrices such that $AB=I$ and $|A|=\dfrac18$ . Then $|\operatorname{adj}(B\operatorname{adj}(2A))|$ is equal to

128

Answer and worked solution

Official answer: C

Determinants. $B=A^{-1}$ , so $|B|=8$ . $|\operatorname{adj}(2A)|=|2A|^2=(8\cdot\frac18)^2=1$ .

Product. $|B\operatorname{adj}(2A)|=8$ , and $|\operatorname{adj}M|=|M|^2=64$ .

(C)

Topics:Adjoint and inverse

JEE Main 2022 · 27 Jun · Shift 2, Mathematics question 4