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Let A and B be two square matrices satisfying `A+BA^(T)=I` and `B+AB^(T)=I` and `O` is null matrix then identity the correct statement.A. `A=B^(T)`B. `B=A^(T)`C. `A^(4)-2A^(2)+A=O`D. `A^(4)-2A^(2)-A=O` |
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Answer» Correct Answer - A::B::C `A+BA^(T)=I` and `B+AB^(T)=I` `impliesA^(T)+AB^(T)=I` and `B^(T)+BA^(T)=I` `impliesA^(T)+I-B=I` and `B^(T)+I-A=I` `impliesA^(T)=B` and `B^(T)=A` Now `A+BA^(T)=I` and `B+AB^(T)=I` `impliesA+B^(2)=I` and `B+A^(2)=I` `impliesA+(I-A^(2))^(2)=I` |
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