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નીચે આપેલા શ્રેણિક $\mathrm{A}$ અને $\mathrm{B}$ માટે ચકાસો કે $(\mathrm{A} \mathrm{B})^{\prime}=\mathrm{B}^{\prime} \mathrm{A}^{\prime}$ : $\mathrm{A}=\left[\begin{array}{l}0 \\ 1 \\ 2\end{array}\right], \mathrm{B}=\left[\begin{array}{lll}1 & 5 & 7\end{array}\right]$.
Solution
$A B=\left[\begin{array}{l}0 \\ 1 \\ 2\end{array}\right]\left[\begin{array}{lll}1 & 5 & 7\end{array}\right]=\left[\begin{array}{ccc}0 & 0 & 0 \\ 1 & 5 & 7 \\ 2 & 10 & 14\end{array}\right]$
$\therefore(A B)^{\prime}=\left[\begin{array}{lll}0 & 1 & 2 \\ 0 & 5 & 10 \\ 0 & 7 & 14\end{array}\right]$
Now, $A^{\prime}=\left[\begin{array}{lll}0 & 1 & 2\end{array}\right], B^{\prime}=\left[\begin{array}{l}1 \\ 5 \\ 7\end{array}\right]$
$\therefore B ^{\prime} A^{\prime}=\left[\begin{array}{l}1 \\ 5 \\ 7\end{array}\right]\left[\begin{array}{lll}0 & 1 & 2\end{array}\right]=\left[\begin{array}{lll}0 & 1 & 2 \\ 0 & 5 & 10 \\ 0 & 7 & 14\end{array}\right]$
Hence, we have verified that $(A B)^{\prime}=B^{\prime} A^{\prime}$.
