JEE Main 2022 · 28 Jun · Shift 1 · Mathematics Q4

← JEE Main 2022 · 28 Jun · Shift 1

MathematicsSingle correct+4 / -1Question 4 of 90

Let $A$ be a matrix of order $3\times3$ and $\det(A)=2$ . Then $\det\left(\det(A)\operatorname{adj}\left(5\operatorname{adj}\left(A^3\right)\right)\right)$ is equal to ______.

512\times10^6

256\times10^6

1024\times10^6

256\times10^{11}

Answer and worked solution

Official answer: A

Rules for $3\times3$ . $\operatorname{adj}(kM)=k^2\operatorname{adj}M$ and $|\operatorname{adj}(\operatorname{adj}B)|=|B|^4$ .

So $|\operatorname{adj}(5\operatorname{adj}A^3)|=25^3\cdot|A^3|^4=15625\cdot8^4$ , and multiplying by $|A|=2$ gives a factor $2^3$ :
$8\cdot15625\cdot4096=512\times10^6.$

(A)

Topics:Adjoint and inverse Determinants and properties

← Previous question Next question →

JEE Main 2022 · 28 Jun · Shift 1, Mathematics question 4