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Question
For non-singular square matrix A, B and C of the same order \[\left( A B^{- 1} C \right) =\] ______________ .
Options
\[A^{- 1} B C^{- 1}\]
\[C^{- 1} B^{- 1} A^{- 1}\]
\[CB A^{- 1}\]
\[C^{- 1} BA^{- 1}\]
Solution
\[C^{- 1} B A^{- 1}\]
We have,
\[\left( A B^{- 1} C \right)^{- 1} = C^{- 1} \left( B^{- 1} \right)^{- 1} A^{- 1} \]
\[ = C^{- 1} B A^{- 1}\]
Notes
In Quesion, We are to find the inverse of \[\left( A B^{- 1} C \right)\] . The inverse is missing in the question.
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