InterviewSolution
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InterviewSolution
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If `A` and `B` are invertible matrices then which of the following is not correct?A. `adjA=|A|.A^(-1)`B. `det(A)^(-1)=["det"(A)]^(-1)`C. `(AB)^(-1)=B^(-1)A^(-1)`D. `(A+B)^(-1)=B^(-1)+A^(-1)` |
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Answer» Correct Answer - D Since A and B are invertible matrices So we can say that `(AB)^(-1)=B^(-1)A^(-1)`…………..i Also `A^(-1)=1/(|A|)(adjA)` `implies adjA=|A|.A^(-1)`………….ii Also `det(A)^(-1)=[det(A)]^(-1)` `implies det(A)^(-1)=1/([det(A)])` `implies det(A).det(A)^(-1)=1`...............iii which is true Again `(A+B)^(-1)=1/(|(A+B)|)(adj(A+B)` `implies (A+B)^(-1)!=B^(-1)+A^(-1)`..........iv So only option (d) is incorrect |
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