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Skew Hermitian Matrix

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If the matrices A,B and A+B are invertible then [A(A+B)^-1 B]^-1 is equal to

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Q. If A and B are invertible matrices, then which one of the following is not correct?
(a) adj A =

|A|

A^-1 (b) det (A^-1) = [det(A)]^-1
(c) (AB)^-1 = B^-1A^-1 (d) (A+B)^-1 = B^-1 + A^-1

Q. If A and B are invertible matrices of order 3,

| A | = 2

{| (A B) |}^{- 1} | = - \frac{1}{6}

Q. If the matrices

A, B, (A + B)

are non singular then

{[A {(A + B)}^{- 1} B]}^{- 1}

Q. If A and B are invertible matrices, which of the following statement is not correct.
(a)

adj A = |A| A^{- 1}

\det (A^{- 1}) = {(\det A)}^{- 1}

{(A + B)}^{- 1} = A^{- 1} + B^{- 1}

{(A B)}^{- 1} = B^{- 1} A^{- 1}

A

B

are invertible matrices of order

3, | A | = 2

∣ ∣ {(A B)}^{- 1} ∣ ∣ = - \frac{1}{6}

| B |

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