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If the matrices, A, B and (A+B) are non-...

If the matrices, A, B and `(A+B)` are non-singular, then prove that `[A(A+B)^(-1) B]^(-1) =B^(-1)+A^(-1)`.

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To prove that \([A(A+B)^{-1} B]^{-1} = B^{-1} + A^{-1}\), we will start by manipulating the left-hand side of the equation step by step. ### Step-by-Step Solution: 1. **Start with the left-hand side:** \[ LHS = [A(A+B)^{-1} B]^{-1} \] ...
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If the matrices, A ,B ,(A+B) are non-singular, then prove that [A(A+B)^(-1)B]^(-1)=B^(-1)+A^(-1) .

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Knowledge Check

  • If A,B,C are non - singular matrices of same order then (AB^(-1)C)^(-1)=

    A
    A) `CBA^(-1)`
    B
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    C
    C) `C^(-1)BA^(-1)`
    D
    D) `C^(-1)BA`

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