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# Compute the indicated products: $(iii)\;\begin{bmatrix}1 & -2\\2 & 3\end{bmatrix}\begin{bmatrix}1 & 2 & 3\\2 & 3 & 1\end{bmatrix}$

This question has 6 parts and each part has been answered separately here.

Toolbox:
• Multiplication of two matrices is defined only if the number of columns of the left matrix is the same as the number of rows of the right matrix.
• If A is an m-by-n matrix and B is an n-by-p matrix, then their matrix product AB is the m-by-p matrix whose entries are given by dot product of the corresponding row of A and the corresponding column of B:
• $\begin{bmatrix}AB\end{bmatrix}_{i,j} = A_{i,1}B_{1,j} + A_{i,2}B_{2,j} + A_{i,3}B_{3,j} ... A_{i,n}B_{n,j}$
$\begin{bmatrix}1 & -2\\2 & 3\end{bmatrix}\begin{bmatrix}1 & 2 & 3\\2 & 3 & 1\end{bmatrix} = \begin{bmatrix}1\times 1+-2\times 2 & 1\times 2+-2\times 3 & 1\times 3+-2\times 1\\2\times 1+3\times 2 & 2\times 2+3\times 3 & 2\times 3+3\times 1\end{bmatrix}$
$\begin{bmatrix}1 & -2\\2 & 3\end{bmatrix}\begin{bmatrix}1 & 2 & 3\\2 & 3 & 1\end{bmatrix} = \begin{bmatrix} 1-4 & 2-6 & 3-2\\2+6 & 4+9 & 6+3 \end{bmatrix}$
$\begin{bmatrix}1 & -2\\2 & 3\end{bmatrix}\begin{bmatrix}1 & 2 & 3\\2 & 3 & 1\end{bmatrix} = \begin{bmatrix} -3 & -4 & 1\\8 & 13& 9 \end{bmatrix}$