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JEE Main 202622 JanuaryMorning Shift
Exam
JEE Main
Year
2026
Date
22 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Matrices

JEE Main 2026 · 22 January · Morning Shift · Mathematics · Matrices

If A=[ array ll 2 & 3 3 & 5 array ] , then the determinant of the...

If \mathrm{A}=\left[2335\begin{array}{ll}2 & 3 \\ 3 & 5\end{array}\right], then the determinant of the matrix \left(\mathrm{A}^{2025}-3 \mathrm{~A}^{2024}+\mathrm{A}^{2023}\right)$ is

Options

  1. A12
  2. B28
  3. C24
  4. D16

Correct answer

D. 16

Step-by-step solution

A=[2335]⇒A2=[13212134]A = \begin{bmatrix} 2 & 3 \\ 3 & 5 \end{bmatrix} \Rightarrow A^2 = \begin{bmatrix} 13 & 21 \\ 21 & 34 \end{bmatrix}
∣A2025−3A2024+A2023∣|A^{2025} - 3A^{2024} + A^{2023}|
=∣A2023(A2−3A+I)∣= \left| A^{2023} \left( A^2 - 3A + I \right) \right|
=∣A∣2023∣A2−3A+I∣= |A|^{2023} |A^2 - 3A + I|
=1⋅∣8121220∣=160−144=16= 1 \cdot \begin{vmatrix} 8 & 12 \\ 12 & 20 \end{vmatrix} = 160 - 144 = 16
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