If A and B are two non-zero n n matrics such that A ^2+ B = A ^2 … - Vidyadip

MCQ

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

A
$AB = I$
B
$A ^2 B = I$
C
$A ^2= I$ or $B = I$
✓
$A ^2 B = BA ^2$

✓

Answer

Correct option: D.

$A ^2 B = BA ^2$

d
$A^2+B=A^2 B$

$\left(A^2-I\right)(B-I)=I$

$A^2+B=A^2 B$

$A^2(B-I)=B$

$A^2=B(B-I)^{-1}$

$A^2=B\left(A^2-I\right)$

$A^2=B A^2-B$

$A^2+B=B A^2$

$A^2 B=B A^2$

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