Question

The sum and product of matrices A and B exist. Which of the following implications are necessarily true ?
1. A and B are square matrices of same order.
2. A and B are non-singular matrices.
Select the correct answer using the code given below :

• A. 1 only
• B. 2 only
• C. Both 1 and 2
• D. Neither 1 nor 2

Answer 1

The correct option is A 1 only

For sum to exist both the matrix necessarily has to be of the same order.

If product exist and determinant is $0$, then one or both the matrix may have their determinant $0$. So it's not necessarily true that both will be non-singular.

Hence, A is correct.