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Friday, 9 October

JEE Main Maths · Determinants

Trap involving |adj(A)| vs |A^-1|

Trap involving |adj(A)| vs |A^-1| (Determinants) was asked 6 times in 6 JEE Main shifts, 2022–2026, out of the 42 shifts Lumi analysed.

Times asked
6
in 6 shifts
Years
2022–2026
Usual format
Single correct
Multi-step
Pattern
Frequent
repeats across shifts

How it is asked

  • Evaluate nested adjoint and inverse of matrix
  • Determinant of adjoint of matrix expression

Difficulty

Easy 0Medium 4Hard 2

Where it sits

Chapter: Determinants. Topic: Matrix Inverse, 22 questions over 7 ideas.

Other repeat ideas in this topic

Every time it came

All 6 questions

Newest first, each with its options and official answer.

  1. 5 Apr 2026, Shift 1 · Q3Let A be a 3×33 \times 3 matrix such that AT[101]=[522]A^T\begin{bmatrix}1\\0\\1\end{bmatrix}=\begin{bmatrix}5\\2\\2\end{bmatrix},…HardSingle correct
  2. 2 Apr 2025, Shift 1 · Q15Let a∈Ra\in\mathbf{R} and A be a matrix of order 3×33\times3 such that det⁡(A)=−4\det(A)=-4 and…MediumSingle correct
  3. 3 Apr 2025, Shift 1 · Q5Let AA be a matrix of order 3×33 \times 3 and ∣A∣=5|A| = 5. If ∣2 adj(3A adj(2A))∣=2α⋅3β⋅5γ|2\,adj(3A\,adj(2A))| = 2^{\alpha}\cdot 3^{\beta}\cdot 5^{\gamma},…MediumSingle correct
  4. 13 Apr 2023, Shift 2 · Q5Let for A=[123α31112]A=\begin{bmatrix}1&2&3\\ \alpha&3&1\\ 1&1&2\end{bmatrix}, ∣A∣=2|A|=2. If ∣2 adj(2 adj(2A))∣=32n|2\,\mathrm{adj}(2\,\mathrm{adj}(2A))|=32^n, then…MediumSingle correct
  5. 28 Jul 2022, Shift 1 · Q14Let the matrix A=[010001100]A=\begin{bmatrix}0&1&0\\0&0&1\\1&0&0\end{bmatrix} and the matrix B0=A49+2A98B_0=A^{49}+2A^{98}. If Bn=Adj(Bn−1)B_n=\mathrm{Adj}(B_{n-1}) for…HardSingle correct
  6. 24 Jun 2022, Shift 1 · Q9Let S={n:1≤n≤50S = \{\sqrt{n} : 1 \le n \le 50 and n is odd}\}. Let a∈Sa \in S and…MediumSingle correct