Does AB Exist? Find Its Order

Given:

\[ A \text{ is of order } m \times n, \quad B \text{ is of order } n \times p \]

Condition for Existence of AB:

Matrix multiplication \(AB\) exists if the number of columns of A equals the number of rows of B.

\[ \text{Since } n = n, \quad AB \text{ exists} \]

Order of AB:

\[ AB \text{ will be of order } m \times p \]

Final Answer:

\[ AB \text{ exists and its order is } m \times p \]

Conclusion:

The product of an m×n matrix and an n×p matrix always exists and results in an m×p matrix.