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MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES3 Marks
Question
Given, $\text{A}=\begin{bmatrix}2&4&0\\3&9&6\end{bmatrix}$ and $\text{B}=\begin{bmatrix}1&4\\2&8\\1&3\end{bmatrix}$ is $(\text{AB})'=\text{B}'\text{A}'\ ?$
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Answer

We have, $\text{A}=\begin{bmatrix}2&4&0\\3&9&6\end{bmatrix}$ and $\text{B}=\begin{bmatrix}1&4\\2&8\\1&3\end{bmatrix}$
$\therefore\ \text{AB}=\begin{bmatrix}2+8+0&8+32+0\\3+18+6&12+72+18\end{bmatrix}$
$\Rightarrow\ \text{AB}=\begin{bmatrix}10&40\\27&102\end{bmatrix}$
$\Rightarrow\ (\text{AB})'=\begin{bmatrix}10&27\\40&102\end{bmatrix}$
Also, $\text{B}'=\begin{bmatrix}1&2&1\\4&8&3\end{bmatrix}$ and $\text{A}'=\begin{bmatrix}2&3\\4&9\\0&6\end{bmatrix}$
$\therefore\ \text{B}'\text{A}'=\begin{bmatrix}2+8+0&3+18+6\\8+32+0&12+72+18\end{bmatrix}$
$=\begin{bmatrix}10&27\\40&102\end{bmatrix}$
$\therefore\ (\text{AB})'=\text{B}'\text{A}'$

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