Question

If $A$ and $B$ are two non-zero $n \times n$ matrics such that $A ^2+ B = A ^2 B$, then

• A. $A ^2= I$ or $B = I$
• B. $A ^2 B = BA ^2$
• C. $AB = I$
• D. $A ^2 B = I$

Answer 1

Answer: (B)

$A ^2 B = BA ^2$

Answer 2

A2+B=A2B
(A2-I)(B-I)=I.......(1)
A2+B=A2B
A2(B-I)=B
A2=B(B-I)-1
A2=B(A2-I)
A2=BAA2-B
A2+B=BA2
A2B=BA2