JEE Main Maths · Matrices

Powers of Square Matrices

Powers of Square Matrices (Matrices) was asked 6 times in 6 JEE Main shifts, 2021–2025, out of the 42 shifts Lumi analysed. 4 of the 6 had a numerical answer.

Times asked: 6; in 6 shifts
Years: 2021–2025
Usual format: Numerical value; Multi-step
Pattern: Asked most years; repeats across shifts

How it is asked

Sum of elements of high matrix power from recurrence
Count n with matrix power identity

Difficulty

Easy 0Medium 3Hard 3

Where it sits

Chapter: Matrices. Topic: Matrix Multiplication, 19 questions over 11 ideas.

All 6 questions

Newest first, each with its options and official answer.

4 Apr 2025, Shift 2 · Q4Let 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…HardSingle correct
8 Apr 2024, Shift 1 · Q22Let $A=\begin{bmatrix}2&-1\\1&1\end{bmatrix}$ . If the sum of the diagonal elements of $A^{13}$ is $3^n$ , then $n$ is equal to ____________.MediumNumerical value
11 Apr 2023, Shift 1 · Q29Let $A = \begin{bmatrix} 0 & 1 & 2 \\ a & 0 & 3 \\ 1 & c & 0 \end{bmatrix}$ , where $a, c \in \mathbb{R}$ . If $A^3 = A$ and the positive…HardNumerical value
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
29 Jun 2022, Shift 1 · Q10Let $A = [a_{ij}]$ be a square matrix of order 3 such that $a_{ij} = 2^{j-i}$ , for all $i, j = 1, 2, 3$ . Then, the matrix…MediumSingle correct
25 Jul 2021, Shift 1 · Q87Let…MediumNumerical value