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Friday, 9 October

JEE Main Maths · Matrices

Cayley-Hamilton Theorem Application

Cayley-Hamilton Theorem Application (Matrices) was asked 4 times in 4 JEE Main shifts, 2024–2026, out of the 42 shifts Lumi analysed.

Times asked
4
in 4 shifts
Years
2024–2026
Usual format
Single correct
Multi-step
Pattern
New since 2024
repeats across shifts

How it is asked

  • Count correct statements on matrix identities
  • Reduce matrix power using polynomial relation

Difficulty

Easy 0Medium 2Hard 2

Where it sits

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

Other repeat ideas in this topic

Every time it came

All 4 questions

Newest first, each with its options and official answer.

  1. 2 Apr 2026, Shift 1 · Q4Let A=[121α]A=\begin{bmatrix}1&2\\1&\alpha\end{bmatrix} and B=[33β2]B=\begin{bmatrix}3&3\\\beta&2\end{bmatrix}. If A2−4A+I=OA^2-4A+I=O and B2−5B−6I=OB^2-5B-6I=O,…HardOther
  2. 2 Apr 2025, Shift 2 · Q3Let AA be a 3×33\times3 real matrix such that A2(A−2I)−4(A−I)=OA^2(A-2I) - 4(A-I) = O, where II and OO are the identity and null matrices,…MediumSingle correct
  3. 8 Apr 2024, Shift 1 · Q4Let A=[2a013105b]A=\begin{bmatrix}2&a&0\\1&3&1\\0&5&b\end{bmatrix}. If A3=4A2−A−21IA^3=4A^2-A-21I, where II is the identity matrix of order 3×33\times3, then…MediumSingle correct
  4. 9 Apr 2024, Shift 2 · Q4Let B=[1315]B=\begin{bmatrix}1&3\\1&5\end{bmatrix} and AA be a 2×22\times2 matrix such that AB−1=A−1AB^{-1}=A^{-1}. If BCB−1=ABCB^{-1}=A and…HardSingle correct