JEE Main 2022 · 26 Jun · Shift 1 · Mathematics Q3

MathematicsSingle correct+4 / -1Question 3 of 90

Let A be a $3\times3$ invertible matrix. If $|\operatorname{adj}(24A)|=|\operatorname{adj}(3\operatorname{adj}(2A))|$ , then $|A|^2$ is equal to :

6^6

2^{12}

2^6

Answer and worked solution

Official answer: C

Facts for $3\times3$ . $|\operatorname{adj}M|=|M|^2$ and $\operatorname{adj}(kM)=k^2\operatorname{adj}M$ .

Left. $|\operatorname{adj}(24A)|=\left(24^3|A|\right)^2=24^6|A|^2$ .

Right. $3\operatorname{adj}(2A)=12\operatorname{adj}A$ , so $|\operatorname{adj}(12\operatorname{adj}A)|=\left(12^3|A|^2\right)^2=12^6|A|^4$ .

Solve. $|A|^2=\dfrac{24^6}{12^6}=2^6$ .

(C)

Topics:Adjoint and inverse Determinants and properties

JEE Main 2022 · 26 Jun · Shift 1, Mathematics question 3