If A - B and C are 3 invertible matrices and BAC - I- what is the value of A-A- CBB- C -1 B -1C- B -1 C -1D- A -1

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Inverse of a Matrix

If A , B and ...

Question

If A, B and C are 3 invertible matrices and BAC = I, what is the value of A.

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C^{- 1} B^{- 1}

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B^{- 1} C^{- 1}

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A^{- 1}

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A, B

C

B A C = I,

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|

If A and B are invertible matrices, then which of the following is not correct?

(a) $a d j A = | A | . A^{- 1}$
(b) $d e t (A)^{- 1} = [d e t (A)]^{- 1}$
(c) $(A B)^{- 1} = B^{- 1} A^{- 1}$
(d) $(A + B)^{- 1} = B^{- 1} + A^{- 1}$

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