If matrices $A =\begin{bmatrix}1&2&3\end{bmatrix}$ and $B =\begin{bmatrix}1\\2\\3\end{bmatrix}$ then BA is equal to

$\begin{bmatrix}1&2&3\\2&4&6\\3&6&9\end{bmatrix}$

The correct answer is Option (3) → $\begin{bmatrix}1&2&3\\2&4&6\\3&6&9\end{bmatrix}$

Given

$A=\begin{pmatrix}1&2&3\end{pmatrix},\quad B=\begin{pmatrix}1\\2\\3\end{pmatrix}$

Then

$BA=\begin{pmatrix}1\\2\\3\end{pmatrix}\begin{pmatrix}1&2&3\end{pmatrix}$

$=\begin{pmatrix} 1\cdot 1 & 1\cdot 2 & 1\cdot 3\\ 2\cdot 1 & 2\cdot 2 & 2\cdot 3\\ 3\cdot 1 & 3\cdot 2 & 3\cdot 3 \end{pmatrix}$

$=\begin{pmatrix} 1&2&3\\ 2&4&6\\ 3&6&9 \end{pmatrix}$

Final answer: $\begin{pmatrix}1&2&3\\2&4&6\\3&6&9\end{pmatrix}$