**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 $B$

$=m \times p$