Question

Which of the following is not correct?

• A. If \( A \) and \( B \) are two matrices of order \( 2 \times 3 \) and \( 3 \times 4 \) respectively, then their product \( AB \) is of order \( 2 \times 4 \).
• B. If \( A \) and \( B \) are square matrices of the same order, then \( AB = BA \).
• C. The augmented matrix of the system of linear equations in matrix form \( Ax = B \) is given by \( (A|B) \).
• D. Any homogeneous system of linear equations has at least one solution.

Hint:

Remember that matrix multiplication is not commutative unless A and B commute.

Answer 1

The Correct Option is B

Matrix multiplication is associative, yet not generally commutative. Therefore, the property \( AB = BA \) does not universally apply to square matrices \( A \) and \( B \).