Q. If $A$ and $B$ are two matrices such that $A B=B$ and $B A=A$, then $A^{2}+B^{2}=$

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A

$2 A B$

B

$2 BA$

C

$A B$

D

$A+B$

Solution:

$A^{2}+B^{2}=A A+B B=A(B A)+B(A B)=(A B) A+(B A) B=B A+A B=A+B$

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