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Compute the products \( A B \) and \( B A \) whichever exists in each of the following cases:
\[
A=\left[\begin{array}{rr}
1 & -2 \\
2 & 3
\end{array}\right] \text { and } B=\left[\begin{array}{ccc}
1 & 2 & 3 \\
2 & 3 & 1
\end{array}\right] \text {, }
\]
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