If AB=A, BA=B then A2+B2= - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

A
$A + B$
B
$A - B$
C
$AB$
D
$O$

Solution:

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

If $AB = A, BA = B$ then $A^{2} + B^{2} =$

Solution:

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