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

MathematicsSingle correct+4 / -1Question 4 of 90

Let $A=\begin{pmatrix}4&-2\\\alpha&\beta\end{pmatrix}$ .

If $A^2+\gamma A+18I=O$ , then $\det(A)$ is equal to ______.

-18

-50

Answer and worked solution

Official answer: B

Cayley-Hamilton. $A^2-(\operatorname{tr}A)A+(\det A)I=O$ . Since A is not scalar, comparing with $A^2+\gamma A+18I=O$ gives $\det A=18$ .

(B)

Topics:Matrix algebra

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