Let $\mathrm{A}+2\mathrm{B}=\left[\begin{array}{ccc}1& 2& 0\\ 6& -3& 3\\ -5& 3& 1\end{array}\right] \mathrm{and} 2\mathrm{A}-\mathrm{B}=\left[\begin{array}{ccc}2& -1& 5\\ 2& -1& 6\\ 0& 1& 2\end{array}\right].$ If Tr(A) denotes the
sum of all diagonal elements of the matrix A, then Tr(A) – Tr(B) has value equal to :

$\begin{array}{rcl}\mathrm{A}+2\mathrm{B}+4\mathrm{A}-2\mathrm{B}& =& \left[\begin{array}{ccc}1& 2& 0\\ 6& -3& 3\\ -5& 3& 1\end{array}\right]+\left[\begin{array}{ccc}4& -2& 10\\ 4& -2& 12\\ 0& 2& 4\end{array}\right]\\ 5\mathrm{A}& =& \left[\begin{array}{ccc}5& 0& 10\\ 10& -5& 15\\ -5& 5& 5\end{array}\right]\\ \mathrm{A}& =& \left[\begin{array}{ccc}1& 0& 2\\ 2& -1& 3\\ -1& 1& 1\end{array}\right]\\ 2\mathrm{B}& =& \left[\begin{array}{ccc}1& 2& 0\\ 6& -3& 3\\ -5& 3& 1\end{array}\right]-\left[\begin{array}{ccc}1& 0& 2\\ 2& -1& 3\\ -1& 1& 1\end{array}\right]\\ & =& \left[\begin{array}{ccc}0& 2& -2\\ 4& -2& 0\\ -4& 2& 0\end{array}\right]\\ \mathrm{B}& =& \left[\begin{array}{ccc}0& 1& -1\\ 2& -1& 0\\ -2& 1& 0\end{array}\right]\\ \therefore \mathrm{Tr}\left(\mathrm{A}\right)-\mathrm{Tr}\left(\mathrm{B}\right)& =& 1+1\\ & =& 2\end{array}$