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Question
If A and B are invertible matrices, which of the following statement is not correct.
Options
\[adj A = \left| A \right| A^{- 1}\]
\[\det \left( A^{- 1} \right) = \left( \det A \right)^{- 1}\]
\[\left( A + B \right)^{- 1} = A^{- 1} + B^{- 1}\]
\[\left( AB \right)^{- 1} = B^{- 1} A^{- 1}\]
Solution
\[\left( A + B \right)^{- 1} = A^{- 1} + B^{- 1}\]
We have, \[adj A = \left| A \right| A^{- 1}\], \[\det \left( A^{- 1} \right) = \left( \det A \right)^{- 1}\] and \[\left( AB \right)^{- 1} = B^{- 1} A^{- 1}\] all are the properites of inverse of a matrix.
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