Let $A=\begin{pmatrix}1&2\ 0&1\end{pmatrix}$ and $B=\begin{pmatrix}2&0\ 1&3\end{pmatrix}$

Question

Let $A=\begin{pmatrix}1&2\ 0&1\end{pmatrix}$ and $B=\begin{pmatrix}2&0\ 1&3\end{pmatrix}$. Calculate $AB$ and $BA$.[4] Use your results to explain why reversing the order of multiplication is not valid in general.[1]

Accepted Answer

(a) $AB=\begin{pmatrix}4&6\ 1&3\end{pmatrix}$, $BA=\begin{pmatrix}2&4\ 1&5\end{pmatrix}$. (b) The products differ.

Comparing the two orders of multiplication

Comparing the two orders of multiplication

Solution:

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