Question

If A and B are any two different square matrices of order n with A – B is non-singular $A^3=B^3$ and A(AB) = B(BA) , then

• A. $A^2+B^2=O$
• B. $A^2+B^2=I$
• C. $A^2+B^3=I$
• D. $A^3+B^3=O$

Answer 1

The correct option is A $A^2+B^2=O$

$A^3=B^3.....\left(i\right)$
$A^{2}B=B^{2}A.........\left(ii\right)$
$(A^2+B^2)(A-B)=0$
$\because |A-B|\ne 0$
$A^2+B^2=0$