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Q.

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

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a

A=I

b

B=I

c

AB=BA

d

AB=I

answer is C.

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Detailed Solution

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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