A and B are two non-singular square matrices of order 3×3 such that AB = A and BA = B then
A
|A−B|=6
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B
|A+B|=0
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C
|A−B|2=0
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D
|A+B|=8
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Solution
The correct options are B|A+B|=0 C|A−B|2=0 D|A+B|=8 AB=A,BA=B(A+B)2=A2+B2+AB+BA⇒A2=AA=2(A+B)=ABA=AB=A|A+B|2=8|A+B|SimilarlyB2=B⇒|A+B|(|A+B|−8)=0⇒|A+B|=0or⇒|A+B|=8Similarly|A+B|2=0