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Question

If A and B are square matrices of same order satisfying A+B=AB, then


A
AB=BA
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B
AB=BA 
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C
A+B=BA
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D
AB=BA
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Solution

The correct option is C AB=BA
Given, A+B=AB     (1) 
ABAB+I=I
(IA)(IB)=I
IA and IB are inverse of each other.
So, (IB)(IA)=I
IAB+BA=I
A+B=BA     (2)

From (1) and (2),
AB=BA

Mathematics

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