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\begin{document}

{\bf Question}

Evaluate $A+B,\ A-B$ and $B-A$ where

\begin{description}
\item[(i)]
$A=\left(\begin{array}{cc} 2 &amp; 1\\ 9 &amp; 7\end{array}\right);\ \
B=\left(\begin{array} {cc} -6 &amp; 3\\ 1 &amp; 8 \end{array} \right)$

\item[(ii)]
$A=\left(\begin{array}{cc} 7 &amp; 1\\ -3 &amp; 6\\ 6 &amp; -3
\end{array}\right);\ \ B=\left(\begin{array} {cc} 2 &amp; 6\\ 1 &amp; -8\\
2 &amp; 4 \end{array} \right)$
\end{description}

\medskip

{\bf Answer}
\begin{description}
\item[(i)]
$A+B=\left(\begin{array}{cc} 2 &amp; 1\\9 &amp; 7
\end{array}\right)+\left(\begin{array}{cc} -6 &amp; 3\\1 &amp; 8
\end{array}\right)=\left(\begin{array}{cc} -4 &amp; 4\\10 &amp; 15
\end{array}\right)$

$A-B=\left(\begin{array}{cc} 2 &amp; 1\\9 &amp; 7
\end{array}\right)-\left(\begin{array}{cc} -6 &amp; 3\\1 &amp; 8
\end{array}\right)=\left(\begin{array}{cc} 8 &amp; -2\\8 &amp; -1
\end{array}\right)$

$B-A=-(A-B)=\left(\begin{array}{cc} -8 &amp; 2\\-8 &amp; 1
\end{array}\right)$

\item[(ii)]
$A+B=\left(\begin{array}{cc} 7 &amp; 1\\-3 &amp; 6\\6 &amp; -3
\end{array}\right)+\left(\begin{array}{cc} 2 &amp; 6\\1 &amp; -8\\ 2 &amp; 4
\end{array}\right)=\left(\begin{array}{cc} 9 &amp; 7\\-2 &amp; -2\\ 8 &amp; +1
\end{array}\right)$

$A-B=\left(\begin{array}{cc} 7 &amp; 1\\-3 &amp; 6\\6 &amp; -3
\end{array}\right)-\left(\begin{array}{cc} 2 &amp; 6\\1 &amp; -8\\ 2 &amp; 4
\end{array}\right)=\left(\begin{array}{cc} 5 &amp; -5\\-4 &amp; 14\\ 4 &amp; -7
\end{array}\right)$

$B-A=-(A-B)=\left(\begin{array}{cc} -5 &amp; 5\\4 &amp; -14\\-4 &amp; 7
\end{array}\right)$

\end{description}

\end{document}
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