JEE Main 2024 (Online) 29th January Evening ShiftQuestion 1
Let $A=\begin{bmatrix}2&1&2\\6&2&11\\3&3&2\end{bmatrix}$ and $P=\begin{bmatrix}1&2&0\\5&0&2\\7&1&5\end{bmatrix}$. The sum of the prime factors of $\left|P^{-1}AP-2I\right|$ is equal to
Determinant
Solution
$|P^{-1}AP-2I|=|A-2I|=\begin{vmatrix}0&1&2\\6&0&11\\3&3&0\end{vmatrix}=33+36=69=3\cdot23$; sum of prime factors $=26$.