Question:
If $A$ is an $m \times n$ matrix and $B$ is $n \times p$ matrix does $A B$ exist? If yes, write its order.
Solution:
Given: Order of $A=m \times n$
Order of $B=n \times p$
Since the number of columns in $A$ are equal to the number of rows in $B$, i.e. $n, A B$ exists.
Order of $A B=$ Number of rows in $A \times$ Number of columns in $B$
$=m \times p$
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