If A is of order `mxxn` and B is of oredr `pxxq`, then AB is defined only if

Options

A. m=q
B. m=p
C. n=p
D. n=q

Answer

To determine when the product of two matrices \( A \) and \( B \) is defined, we need to consider the dimensions (or orders) of the matrices involved.

1. **Identify the dimensions of the matrices:**
- Let matrix \( A \) be of order \( m \times n \).
- Let matrix \( B \) be of order \( p \times q \).

2. **Condition for matrix multiplication:**
- The product \( AB \) is defined if the number of columns in the first matrix \( A \) (which is \( n \)) is equal to the number of rows in the second matrix \( B \) (which is \( p \)).
- Therefore, the condition for the multiplication \( AB \) to be defined is:
\[ n = p \]

3. **Determine the order of the resulting matrix:**
- If the multiplication \( AB \) is defined, the resulting matrix will have the order of the number of rows of the first matrix and the number of columns of the second matrix.
- Thus, the order of the resulting matrix \( AB \) will be \( m \times q \).

**Final Conclusion:**
- The product \( AB \) is defined only if \( n = p \), and the order of the resulting matrix \( AB \) will be \( m \times q \).