If two matrices A and B are of order `ptimesq and r timess` respectively,then they can be subtracted only if

Options

A. `p=r, q=s`
B. `p=q, r=s`
C. `p=q`
D. `pner, qnes`

Answer

To determine when two matrices A and B can be subtracted, we need to analyze their orders.

1. **Understanding Matrix Orders**:
- Let matrix A be of order \( P \times Q \) (which means it has P rows and Q columns).
- Let matrix B be of order \( R \times S \) (which means it has R rows and S columns).

2. **Condition for Subtraction**:
- For the subtraction of two matrices to be possible, both matrices must have the same dimensions. This means:
- The number of rows in matrix A must be equal to the number of rows in matrix B: \( P = R \)
- The number of columns in matrix A must be equal to the number of columns in matrix B: \( Q = S \)

3. **Conclusion**:
- Therefore, the matrices A and B can be subtracted if and only if:
- \( P = R \) and \( Q = S \)

Based on this analysis, the correct answer is that the subtraction of matrices A and B is possible only if \( P = R \) and \( Q = S \).