1. The problem asks for the order of the product of two matrices $A$ and $B$ where $A$ is of order $m \times n$ and $B$ is of order $n \times p$. 2. The rule for matrix multiplication states that if $A$ is $m \times n$ and $B$ is $n \times p$, then the product $AB$ is defined and the resulting matrix is of order $m \times p$. 3. This is because the inner dimensions $n$ must match for multiplication to be possible, and the resulting matrix takes the outer dimensions $m$ and $p$. 4. Therefore, the product matrix $AB$ is of order $m \times p$. Final answer: D. $m \times p$