JEE Main 29 January 2024, Shift 1, Maths Q4

Question 4 of 90 in this shift, Maths question 4 of 30, Section A.

Let A be a square matrix such that

AA^T=I

. Then

\frac{1}{2}A\left[(A+A^T)^2+(A-A^T)^2\right]

is equal to

(1) $A^2+A^T$
(2) $A^3+A^T$ Official answer
(3) $A^2+I$
(4) $A^3+I$

Official answer

Option 2

NTA final key.

Chapter: Matrices
Topic: Matrix Multiplication
Idea tested: Orthogonal Matrix Multiplication Definition

Same idea in other shifts

Asked 2× in all

25 Feb 2021, Shift 2 · Q61If for the matrix, $A = \begin{bmatrix} 1 & -\alpha \\ \alpha & \beta \end{bmatrix}$ , $AA^T = I_2$ , then the value of $\alpha^4 + \beta^4$ …EasySingle correct

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 108 of the 174 JEE Main shifts held from 2017 to 2026.