Suppose P and Q are two different matrices of order `3xx n " and" n xx p`, then the order of the matrix `P xx Q` is ?

Options

A. `3 xx p`
B. `p xx 3`
C. `n xx n`
D. `3 xx 3`

Explanation

To find the order of the matrix \( P \times Q \), we need to follow these steps:

1. **Identify the order of matrices \( P \) and \( Q \)**:
- Matrix \( P \) is given to be of order \( 3 \times n \).
- Matrix \( Q \) is given to be of order \( n \times p \).

2. **Determine the conditions for matrix multiplication**:
- For two matrices to be multiplied, the number of columns in the first matrix must be equal to the number of rows in the second matrix.
- Here, the number of columns in \( P \) is \( n \) and the number of rows in \( Q \) is also \( n \). Therefore, the multiplication \( P \times Q \) is valid.

3. **Calculate the order of the resulting matrix**:
- The order of the product of two matrices is determined by the number of rows of the first matrix and the number of columns of the second matrix.
- Since \( P \) has 3 rows and \( Q \) has \( p \) columns, the order of the matrix \( P \times Q \) will be \( 3 \times p \).

Thus, the order of the matrix \( P \times Q \) is \( 3 \times p \).