If` A` and` B `are two matrices of the order` 3 xx m` and `3 xx n`, respectively and `m= n,` then order of matrix `(5A-2B)` is (a) `m xx 3` (b) `3 xx 3` (c) `m xx n` (d) `3 xx n`

Options

A. `mxx3`
B. `3xx3`
C. `mxxn`
D. `3xxn`

Explanation

To solve the problem, we need to determine the order of the matrix \(5A - 2B\) given the orders of matrices \(A\) and \(B\).

### Step-by-Step Solution:

1. **Identify the Orders of Matrices**:
- Matrix \(A\) is of order \(3 \times m\).
- Matrix \(B\) is of order \(3 \times n\).
- We are given that \(m = n\).

2. **Determine the Order of \(5A\)**:
- When a matrix is multiplied by a scalar (in this case, 5), the order of the matrix remains unchanged.
- Therefore, the order of \(5A\) is still \(3 \times m\).

3. **Determine the Order of \(2B\)**:
- Similarly, multiplying matrix \(B\) by the scalar 2 does not change its order.
- Thus, the order of \(2B\) is \(3 \times n\).

4. **Check the Orders of \(5A\) and \(2B\)**:
- Since \(m = n\), we can conclude that both \(5A\) and \(2B\) have the same number of columns.
- Specifically, both matrices have the order \(3 \times m\) (or \(3 \times n\)).

5. **Determine the Order of \(5A - 2B\)**:
- The subtraction of two matrices is only defined when they have the same order.
- Since both \(5A\) and \(2B\) have the order \(3 \times m\) (or \(3 \times n\)), the order of the resulting matrix \(5A - 2B\) will also be \(3 \times m\) (or \(3 \times n\)).

6. **Conclusion**:
- The order of the matrix \(5A - 2B\) is \(3 \times n\) (which is the same as \(3 \times m\) since \(m = n\)).
- Therefore, the correct answer is option (d) \(3 \times n\).