If A = ( * 20 c 1& - 2 &1 2&1&3 ) and B = ( * 20 c 2&1 3&2 1&1 ),… - Vidyadip

MCQ

If $A = \left( {\begin{array}{*{20}{c}}1&{ - 2}&1\\2&1&3\end{array}} \right)$ and $B = \left( {\begin{array}{*{20}{c}}2&1\\3&2\\1&1\end{array}} \right)$, then ${(AB)^T}$ is equal to

A
$\left( {\begin{array}{*{20}{c}}{ - 3}&{ - 2}\\{10}&7\end{array}} \right)$
✓
$\left( {\begin{array}{*{20}{c}}{ - 3}&{10}\\{ - 2}&7\end{array}} \right)$
C
$\left( {\begin{array}{*{20}{c}}{ - 3}&7\\{10}&2\end{array}} \right)$
D
None of these

✓

Answer

Correct option: B.

$\left( {\begin{array}{*{20}{c}}{ - 3}&{10}\\{ - 2}&7\end{array}} \right)$

b
(b) $AB = \left( {\begin{array}{*{20}{c}}
1&{ - 2}&1 \\
2&1&3
\end{array}} \right)$ $\left( {\begin{array}{*{20}{c}}
2&1 \\
3&2 \\
1&1
\end{array}} \right)$= $\left( {\begin{array}{*{20}{c}}
{ - 3}&{ - 2} \\
{10}&7
\end{array}} \right)$

${(AB)^T} = \left( {\begin{array}{*{20}{c}}{ - 3}&{10}\\{ - 2}&7\end{array}} \right)$.

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