JEE Main 2021 · MathsMultiple choiceSingle correctMediumConceptual

JEE Main 22 July 2021, Shift 2, Maths Q64

Question 64 of 90 in this shift, Maths question 4 of 30, Section A.

Let

\mathrm{A}=[\mathrm{a}_{ij}]

be a real matrix of order

3\times3

, such that

\mathrm{a}_{i1}+\mathrm{a}_{i2}+\mathrm{a}_{i3}=1

, for

i=1, 2, 3

. Then, the sum of all the entries of the matrix

\mathrm{A}^3

is equal to :

(1) $1$
(2) $2$
(3) $3$ Official answer
(4) $9$

Official answer

Option 3

NTA final key.

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

Same idea in other shifts

Asked 21× in all

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8 Apr 2023, Shift 1 · Q5Let $P=\begin{bmatrix}\frac{\sqrt{3}}{2}&\frac{1}{2}\\-\frac{1}{2}&\frac{\sqrt{3}}{2}\end{bmatrix}$ ,…HardSingle correct
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25 Jul 2022, Shift 1 · Q21Let $A=\begin{pmatrix}2&-1&-1\\1&0&-1\\1&-1&0\end{pmatrix}$ and $B=A-I$ . If $\omega=\frac{\sqrt3\,i-1}{2}$ , then the number of elements in…HardNumerical value

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.