हल : दिया हुआ है, कि —
$
\begin{array}{l}
A=\left[\begin{array}{l}
2 \\
4 \\
3
\end{array}\right] \quad B=\left[\begin{array}{lll}
2 & 3 & 4
\end{array}\right] \\
\therefore \quad A B=\left[\begin{array}{l}
2 \\
4 \\
3
\end{array}\right]_{3 \times 1}\left[\begin{array}{lll}
2 & 3 & 4
\end{array}\right]_{1 \times 3}=\left[\begin{array}{ccc}
4 & 6 & 8 \\
8 & 12 & 16 \\
6 & 9 & 12
\end{array}\right] \\
\Rightarrow \quad(A B)^{\prime}=\left[\begin{array}{ccc}
4 & 8 & 6 \\
6 & 12 & 9 \\
6 & 16 & 12
\end{array}\right] \\
B^{\prime}=\left[\begin{array}{l}
2 \\
3 \\
4
\end{array}\right] \\
A^{\prime}=\left[\begin{array}{lll}
2 & 4 & 3
\end{array}\right] \\
\end{array}
$
$\therefore \quad B^{\prime} A^{\prime}=\left[\begin{array}{l}2 \\ 3 \\ 4\end{array}\right]\left[\begin{array}{ll}2 & 4 & 3\end{array}\right]=\left[\begin{array}{ccc}4 & 8 & 6 \\ 6 & 12 & 9 \\ 8 & 16 & 12\end{array}\right]$
(i) & (ii) से
$(A B)^{\prime}=B^{\prime} A^{\prime}$
