$A+B=$ $\left[ {\begin{array}{*{20}{c}}
  1&2&{ – 3} \\ 
  5&0&2 \\ 
  1&{ – 1}&1 
\end{array}} \right]$ $ + \left[ {\begin{array}{*{20}{c}}
  3&{ – 1}&2 \\ 
  4&2&5 \\ 
  2&0&3 
\end{array}} \right]$

$ = \left[ {\begin{array}{*{20}{c}}
  {1 + 3}&{2 – 1}&{ – 3 + 2} \\ 
  {5 + 4}&{0 + 2}&{2 + 5} \\ 
  {1 + 2}&{ – 1 + 0}&{1 + 3} 
\end{array}} \right]$ $ = \left[ {\begin{array}{*{20}{c}}
  4&1&{ – 1} \\ 
  9&2&7 \\ 
  3&{ – 1}&4 
\end{array}} \right]$

$B – C = $ $\left[ {\begin{array}{*{20}{c}}
  3&{ – 1}&2 \\ 
  4&2&5 \\ 
  2&0&3 
\end{array}} \right] – \left[ {\begin{array}{*{20}{c}}
  4&1&2 \\ 
  0&3&2 \\ 
  1&{ – 2}&3 
\end{array}} \right]$

$A + (B – C) = $ $\left[ {\begin{array}{*{20}{r}}
  1&2&{ – 3} \\ 
  5&0&2 \\ 
  1&{ – 1}&1 
\end{array}} \right] + \left[ {\begin{array}{*{20}{r}}
  { – 1}&{ – 2}&0 \\ 
  4&{ – 1}&3 \\ 
  1&2&0 
\end{array}} \right]$

$=$ $\left[ {\begin{array}{*{20}{c}}
  {1 + ( – 1)}&{2 + ( – 2)}&{ – 3 + 0} \\ 
  {5 + 4}&{0 + ( – 1)}&{2 + 3} \\ 
  {1 + 1}&{ – 1 + 2}&{1 + 0} 
\end{array}} \right]$  $ = \left[ {\begin{array}{*{20}{c}}
  0&0&{ – 3} \\ 
  9&{ – 1}&5 \\ 
  2&1&1 
\end{array}} \right]$

$(A+B)-C=$ $\left[ {\begin{array}{*{20}{c}}
  4&1&{ – 1} \\ 
  9&2&7 \\ 
  3&{ – 1}&4 
\end{array}} \right] – \left[ {\begin{array}{*{20}{c}}
  4&1&2 \\ 
  0&3&2 \\ 
  1&{ – 2}&3 
\end{array}} \right]$

$=\left[\begin{array}{ccc}4-4 & 1-1 & -1-2 \\ 9-0 & 2-3 & 7-2 \\ 3-1 & -1-(-2) & 4-3\end{array}\right]$ $=\left[\begin{array}{ccc}0 & 0 & -3 \\ 9 & -1 & 5 \\ 2 & 1 & 1\end{array}\right]$

Hence, we have verified that $A+(B-C)=(A+B)-C$.