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

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$AB$

$O$

$A + B$

$A - B$

answer is A.

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Detailed Solution

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

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