Practicing Success
Practicing Success
CUET Preparation Today
If A and B are any two different square matrices of order n with $A^3 = B^3$ and $A (AB) = B (BA)$, then |
$A^2+ B^2 =O$ $A^2+ B^2 =I$ $A^3+ B^3 =I$ none of these |
$A^2+ B^2 =O$ |
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 $(A^2 + B^2) (A - B) =O$ $⇒A^2 + B^2 = O$ |
