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જો $A$ એ સંમિત શ્રેણિક છે અને $B$ વિસંમિત શ્રેણિક છે કે જેથી $A + B = \left[ {\begin{array}{*{20}{c}}
2&3\\
5&{ - 1}
\end{array}} \right]$ , તો $AB$ મેળવો.
$\left[ {\begin{array}{*{20}{c}} 4&{ - 2}\\ 1&{ - 4} \end{array}} \right]$
$\left[ {\begin{array}{*{20}{c}} 4&{ - 2}\\ { - 1}&{ - 4} \end{array}} \right]$
$\left[ {\begin{array}{*{20}{c}} { - 4}&2\\ 1&4 \end{array}} \right]$
$\left[ {\begin{array}{*{20}{c}} { - 4}&{ - 2}\\ { - 1}&4 \end{array}} \right]$
Solution
$A = A',B = B'$
$A + B = \left[ {\begin{array}{*{20}{c}}
2&3\\
5&{ – 1}
\end{array}} \right]\,\,\,\,\,\,\,\,….\left( 1 \right)$
$A' + B' = \left[ {\begin{array}{*{20}{c}}
2&5\\
3&{ – 1}
\end{array}} \right]\,\,\,$
$A – B = \left[ {\begin{array}{*{20}{c}}
2&5\\
3&{ – 1}
\end{array}} \right]\,\,\,\,\,\,\,\,…..\left( 2 \right)$
After addding equation $(1)$ and $(2)$
$A = \left[ {\begin{array}{*{20}{c}}
2&4\\
4&{ – 1}
\end{array}} \right]\,,B = \left[ {\begin{array}{*{20}{c}}
0&{ – 1}\\
1&0
\end{array}} \right]\,$
$AB = \left[ {\begin{array}{*{20}{c}}
4&{ – 2}\\
{ – 1}&{ – 4}
\end{array}} \right]$
