Question

If A and B are square matrices of size n ? n such that $A^2 - B^2 = (A- B)(A+ B)$ , then which of the following will be always true?

• A. A = B
• B. AB = BA
• C. either of A or B is a zero matrix
• D. either of A or B is identity matrix

Answer 1

Answer: (B)

AB = BA

Answer 2

$A^{2} - B^{2} = \left(A -B\right)\left(A+B\right)$ $A^{2} - B^{2} = A^{2} + AB - BA - B^{2}$ $\Rightarrow AB = BA$