JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If \(A=\begin{bmatrix}2&3\\ 3&5\end{bmatrix}\), then the determinant of the matrix \((A^{2025}-3A^{2024}+A^{2023})\) is
- A 28
- B 12
- C 24
- D 16
Answer & Solution
Correct Answer
(D) 16
Step-by-step Solution
Detailed explanation
\(A=\left[\begin{array}{ll}2 & 3 \\ 3 & 5\end{array}\right] \Rightarrow A^2=\left[\begin{array}{ll}13 & 21 \\ 21 & 34\end{array}\right]\) \(\left| A ^{2025}-3 A^{2024}+ A ^{2023}\right|\) \(=\left| A ^{2023}\left(A^2-3 A+ I \right)\right|\)…
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