JEE Main 2026 (Online) 2nd April Evening ShiftQuestion 1
Consider the matrices $A=\begin{bmatrix}2&-2\\4&-2\end{bmatrix}$ and $B=\begin{bmatrix}3&9\\1&3\end{bmatrix}$. If matrices $P$ and $Q$ are such that $PA=B$ and $AQ=B$, then the absolute value of the sum of the diagonal elements of $2(P+Q)$ is $\_\_\_\_\_\_$ .
Matrices
Answer$34$
Solution
$|A|=4\ne0$. $P=BA^{-1}=\begin{pmatrix}-\tfrac{21}2&6\\-\tfrac72&2\end{pmatrix}$, $Q=A^{-1}B=\begin{pmatrix}-1&-3\\-\tfrac52&-\tfrac{15}2\end{pmatrix}$. $\mathrm{tr}P=-\tfrac{17}2$, $\mathrm{tr}Q=-\tfrac{17}2$, so $\mathrm{tr}(2(P+Q))=2(-17)=-34$. Absolute value $=34$.