The order of matrix $A$ is $3 \times 4$ and $B$ is $4 \times 3$. What is the order of $AB$?

Step-by-step Solution:

For matrix multiplication $A_{m\times n} \cdot B_{n\times p}$, the result has order $m \times p$.

Here:

• $A$ is $3 \times 4$ → $m = 3$, $n = 4$
• $B$ is $4 \times 3$ → $n = 4$, $p = 3$

Since inner dimensions match $(n=4)$, multiplication is possible.

$$AB \text{ has order } 3 \times 3$$

Hence, Option B is correct.