JEE Main 2026 (Online) 22nd January Morning ShiftQuestion 1
If $A=\begin{bmatrix}2&3\\3&5\end{bmatrix}$, then the determinant of the matrix $\left(A^{2025}-3A^{2024}+A^{2023}\right)$ is :
Matrices
Solution
$\det A=1$, $\operatorname{tr}A=7$, so $A^2=7A-I$ and $A^2-3A+I=4A$. The matrix is $A^{2023}\cdot4A$, with determinant $1\cdot16\cdot1=16$.