Question

If Tr $\left(A\right)=2+i$, Then Tr $\left[\right(2-i\left)A\right]=$

• A. $2+i$
• B. $2-i$
• C. $3$
• D. $5$

Answer 1

The correct option is D $5$

We know, $\text{Tr}\left(cA\right)=c\cdot \text{Tr}\left(A\right)$, where $c$ is any constant
Here $c=2-i$, which is a complex constant
Hence $\text{Tr}\left[\right(2-i\left)A\right]=(2-i)\text{Tr}\left(A\right)=(2-i)(2+i)=(2^2-i^2)=4-(-1)=5,[\because i^2=-1]$
Thus option 'D' is correct choice.