Let $A+2B=\left[\begin{array}{ccc}1& 2& 0\\ 6& -3& 3\\ -5& 3& 1\end{array}\right]and2A-B=\left[\begin{array}{ccc}2& -1& 5\\ 2& -1& 6\\ 0& 1& 2\end{array}\right]$  , then tr(A) – tr(B) =

$A+2B=\left[\begin{array}{ccc}1& 2& 0\\ 6& -3& 3\\ -5& 3& 1\end{array}\right]$  

tr (A + 2B) = 2 – 3 = –1

tr(A) + 2tr(B) = –1  ………………. (1)

$2A-B=\left[\begin{array}{ccc}2& -1& 5\\ 2& -1& 6\\ 0& 1& 2\end{array}\right]$

$\begin{array}{c}tr\left(2A-B\right)=4-1=3\\ 2tr\left(A\right)-tr\left(B\right)=3\mathrm{.........................}\left(2\right)\end{array}$

Solve (1) & (2),

tr (A) = 1 & tr (B) = –1

$\Rightarrow tr\left(A\right)-tr\left(B\right)=1+1=2$