Find if possible the matrices: a) AB b) BA A=[−1−2−3],B=[123]

Step 1
Given that:
The matrices,
$A=\left[\begin{array}{c}-1\\ -2\\ -3\end{array}\right],B=\left[\begin{array}{ccc}1& 2& 3\end{array}\right]$
Step 2
We know that,
Finding the product of two matrices is only possible when the inner dimension are same , meaning that the number of columns of the first matrix is equal to the number of rows of the second matrix.
a) To find AB :
Let, $A=\left[\begin{array}{c}-1\\ -2\\ -3\end{array}\right],B=\left[\begin{array}{ccc}1& 2& 3\end{array}\right]$
Number of columns of first matrix (A) is 1 .
Number of rows of the second matrix is 1.
To get,
Step 3
Number of columns of $A=$ Number of rows of $B=1$.
Then,
$AB=\left[\begin{array}{c}-1\\ -2\\ -3\end{array}\right]\left[\begin{array}{ccc}1& 2& 3\end{array}\right]=\left[\begin{array}{ccc}-1(1)& (-2)(2)& (-3)(3)\end{array}\right]=\left[\begin{array}{ccc}-1& -4& -9\end{array}\right]$
To get,
$AB=\left[\begin{array}{ccc}-1& -4& -9\end{array}\right]$
b) To find BA :
Number of columns of first matrix B is 3 and number of rows of matrix A is 3 which are equal .
Then,
Step 4
$BA=\left[\begin{array}{ccc}1& 2& 3\end{array}\right]\left[\begin{array}{c}-1\\ -2\\ -3\end{array}\right]=\left[\begin{array}{c}1(-1)+2(-2)+3(-3)\end{array}\right]=\left[\begin{array}{c}-1-4-9\end{array}\right]=\left[\begin{array}{c}-14\end{array}\right]$
Therefore,
a) $AB=\left[\begin{array}{c}-1-4-9\end{array}\right]$
b) $BA=\left[\begin{array}{c}-14\end{array}\right]$

Answer is given below (on video)