JEE Main 2025 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 4 April 2025, Shift 2, Maths Q4

Question 4 of 75 in this shift, Maths question 4 of 25, Section A.

Let the matrix

A=\begin{bmatrix}1&0&0\\1&0&1\\0&1&0\end{bmatrix}

satisfy

A^n=A^{n-2}+A^2-I

for

n\ge 3

. Then the sum of all the elements of

A^{50}

is :

(1)52
(2)53Official answer
(3)44
(4)39

Official answer

Option 2

NTA final key.

Chapter: Matrices
Topic: Matrix Multiplication
Idea tested: Powers of Square Matrices

Same idea in other shifts

Asked 6× in all

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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.