If matrix A is of order 2 × 3 and matrix B is of order 3 × 2, then which of the following is true?

If matrix A is of order 2 × 3 and matrix B is of order 3 × 2, then which of the following is true?

• A. Only AB is defined
• B. Only BA is defined
• C. Both AB and BA are defined and have the same order
• D. Both AB and BA are defined but have different orders

Answer: D) Both AB and BA are defined but have different orders

Explanation: AB will be of order 2 × 2. BA will be of order 3 × 3. Both are defined but have completely different orders.