If A and B are any two different square matrices of order n with $A^3 = B^3$ and $A (AB) = B (BA)$, then
Answer & explanation
Correct answer: option 1
We have,
$(A^2+ B^2) (A-B) = A^3-A^2 B+ B^2 A-B^3$
$=A^3-A (AB) + B (BA) - B^3 =O$
as $A- B≠O$
So $(A^2 + B^2) (A - B) =O$
$⇒A^2 + B^2 = O$