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If $A$ and $B$ are two matrices such that $A + B = A B,$ then

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A=I

B=I

AB=BA

AB=I

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detailed solution

Correct option is C

A+B=AB⇒I−(A+B)+AB=I⇒(I−A)(I−B)=I⇒(I−A)−1=I−B⇒(I−B)(I−A)=I⇒I−(B+A)+BA=I⇒A+B=BAThus, AB=BA

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If A and B are two matrices such that A+B=AB, then

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If $A$ and $B$ are two matrices such that $A + B = A B,$ then