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MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES3 Marks
Question
If $\text{A}=\begin{bmatrix}0&-1&2\\4&3&-4\end{bmatrix}$ and $\text{B}=\begin{bmatrix}4&0\\1&3\\2&6\end{bmatrix},$ then verify that $(\text{AB})'=\text{B}'\text{A}'.$
✓

Answer

We have, $\text{A}=\begin{bmatrix}0&-1&2\\4&3&-4\end{bmatrix}$ and $\text{B}=\begin{bmatrix}4&0\\1&3\\2&6\end{bmatrix}$We have to verify that, $(\text{AB})'=\text{B}'\text{A}'$
$\therefore\ \text{AB}=\begin{bmatrix}3&9\\11&-15\end{bmatrix}$
$\Rightarrow\ (\text{AB})'=\begin{bmatrix}3&11\\9&-15\end{bmatrix}$
and $\text{B}'\text{A}'=\begin{bmatrix}4&1&2\\0&3&6\end{bmatrix}\begin{bmatrix}0&4\\-1&3\\2&-4\end{bmatrix}$$=\begin{bmatrix}3&11\\9&-15\end{bmatrix}$
$=(\text{AB})'$
Hence proved.

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