JEE Main 2025 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 3 April 2025, Shift 2, Maths Q22

Question 22 of 75 in this shift, Maths question 22 of 25, Section B.

Let I be the identity matrix of order

3 \times 3

and for the matrix

A = \begin{bmatrix} \lambda & 2 & 3 \\ 4 & 5 & 6 \\ 7 & -1 & 2 \end{bmatrix}

|A| = -1

. Let

B

be the inverse of the matrix

\mathrm{adj}\left(A\,\mathrm{adj}\left(A^2\right)\right)

. Then

|\lambda B + I|

is equal to __________.

Official answer

38 or -38

NTA final key.

Chapter: Determinants
Topic: Matrix Inverse
Idea tested: Commutativity of Adjoint and Inverse

Same topic in other shifts

All Matrix Inverse questions

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.