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# If $A = \begin{bmatrix} 2 & 4 \\ 3 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 3 \\ -2 & 5 \end{bmatrix}$, then find BA.

Toolbox:
• 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: $\begin{bmatrix}AB\end{bmatrix}_{i,j} = A_{i,1}B_{1,j} + A_{i,2}B_{2,j} + A_{i,3}B_{3,j} ... A_{i,n}B_{n,j}$
Given
A=$\begin{bmatrix}2 & 4\\3& 2\end{bmatrix}$
B=$\begin{bmatrix}1 & 3\\-2 & 5\end{bmatrix}$
BA=$\begin{bmatrix}1 & 3\\-2 & 5\end{bmatrix}\begin{bmatrix}2 & 4\\3& 2\end{bmatrix}$
$\Rightarrow \begin{bmatrix}1(2)+3(3) & 1(4)+3(2)\\-2(2)+5(3) & -2(4)+5(2)\end{bmatrix}$
$\Rightarrow \begin{bmatrix}2+9 & 4+6\\-4+15 & -8+10\end{bmatrix}$
$\Rightarrow \begin{bmatrix}11 & 10\\11 & 2\end{bmatrix}$