Question

If A, B, C are square matrices of the same order, then which of the following is true?

• A. AB = AC
• B. $(AB)^2 = A^2B^2$
• C. AB = 0 $\Rightarrow$ A = 0 or B = 0
• D. AB = I $\Rightarrow$ AB = BA

Answer 1

Answer: (D)

If A, B, C are square matrices of the same order then AB = I $ \Rightarrow $ AB = BA is true because by theory part we see that if AB = identity matrix, then BA must be identity matrix
$\therefore \, AB = I \, \Rightarrow \, AB = BA$