A) \[{{A}^{-1}}B{{C}^{-1}}\]
B) \[{{C}^{-1}}{{B}^{-1}}{{A}^{-1}}\]
C) \[CB{{A}^{-1}}\]
D) \[{{C}^{-1}}B{{A}^{-1}}\]
Correct Answer: D
Solution :
Key Idea: If \[A\] and \[B\] are two non-singular matrices, then\[{{(AB)}^{-1}}={{B}^{-1}}{{A}^{-1}}\]. Since, \[A,\,\,\,B\] and \[C\] are the three non-singular matrices with same order. \[\therefore \] \[{{(A{{B}^{-1}}C)}^{-1}}={{C}^{-1}}{{(A{{B}^{-1}})}^{-1}}\] \[={{C}^{-1}}B{{A}^{-1}}\]1You need to login to perform this action.
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