# Given matrix A and matrix B. Find (if possible) the matrices: (a) AB (b) BA.A=begin{bmatrix}-1 -2-3 end{bmatrix} , B=begin{bmatrix}1 & 2 & 3 end{bmatrix}

Given matrix A and matrix B. Find (if possible) the matrices: (a) AB (b) BA.
$$A=\begin{bmatrix}-1 \\-2\\-3 \end{bmatrix} , B=\begin{bmatrix}1 & 2 & 3 \end{bmatrix}$$

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Step 1
$$A=\begin{bmatrix}-1 \\-2\\-3 \end{bmatrix} , B=\begin{bmatrix}1 & 2 & 3 \end{bmatrix}$$
order of $$A = 3 \times 1$$
order of $$B = 1 \times 3$$
Step 2
a)AB
It is possible and order will be $$3 \times 3$$
$$\begin{bmatrix}-1 \\-2\\-3 \end{bmatrix}\begin{bmatrix}1 & 2 & 3 \end{bmatrix}=\begin{bmatrix}-1 & -2&-3 \\-2& -4&-6\\-3&-6&-9 \end{bmatrix}$$
Step 3
b)BA
It is possible and order will be $$1 \times 1$$
$$\begin{bmatrix}1 & 2 & 3 \end{bmatrix}\begin{bmatrix}-1 \\-2\\-3 \end{bmatrix}$$
$$=\begin{bmatrix}-1 & -4 & -9 \end{bmatrix}$$
$$=\begin{bmatrix}-14 \end{bmatrix}$$