Matrix A ha s m rows and n+ 5 columns; matrix B has m rows and `11 - n` columns. If both AB and BA exist, then (A) AB and BA are square matrix (B) AB and BA are of order `8 xx 8` and `3 xx 13`, respectively (C) `AB=BA` (D) None of these

Explanation

To solve the given problem, we need to analyze the dimensions of matrices A and B and determine the conditions under which the products AB and BA exist.

1. **Identify the dimensions of matrices A and B:**
- Matrix A has \( m \) rows and \( n + 5 \) columns.
- Matrix B has \( m \) rows and \( 11 - n \) columns.

2. **Determine the conditions for the existence of the matrix products AB and BA:**
- For the product \( AB \) to exist, the number of columns in A must equal the number of rows in B. Therefore:
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