JEE Main 2021 (Online) 18th March Morning ShiftQuestion 1
Let $A+2B=\begin{bmatrix}1&2&0\\6&-3&3\\-5&3&1\end{bmatrix}$ and $2A-B=\begin{bmatrix}2&-1&5\\2&-1&6\\0&1&2\end{bmatrix}$. If $\operatorname{Tr}(A)$ denotes the sum of all diagonal elements of the matrix $A$, then $\operatorname{Tr}(A)-\operatorname{Tr}(B)$ has value equal to :
Matrices
Solution
Traces are linear: $\operatorname{Tr}A+2\operatorname{Tr}B=1-3+1=-1$ and $2\operatorname{Tr}A-\operatorname{Tr}B=2-1+2=3$. Solving: $\operatorname{Tr}A=1$, $\operatorname{Tr}B=-1$. $\operatorname{Tr}A-\operatorname{Tr}B=2$. Option (B).