Question:
If $A=\left[\begin{array}{lll}2 & 1 & 4 \\ 4 & 1 & 5\end{array}\right]$ and $B=\left[\begin{array}{rr}3 & -1 \\ 2 & 2 \\ 1 & 3\end{array}\right]$. Write the orders of $A B$ and $B A$.
Solution:
The order of matrix $A$ is $2 \times 3$ and the order of matrix $B$ is $3 \times 2$.
Since the number of columns in $A$ is equal to the number of rows in $B, A B$ exists and it is of order $2 \times 2$. Also, since the number of columns in $B$ is equal to the number of rows in $A, B A$ exists and it is of order $3 \times 3$.
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