| Assertion [A]: \[{{A}^{-1}}\]exists |
| Reason [R]: \[R\left| A \right|=0\] |
A) Both A and R are individually true and R is the correct explanation of A.
B) Both A and R are individually true and R is not the correct explanation of A.
C) 'A' is true but 'R' is false
D) 'A' is false but 'R' is true
E) Both A and R are false.
Correct Answer: C
Solution :
Given Assertion is \[{{A}^{-1}}\]exists We know that \[{{A}^{-1}}\frac{adj\,A}{\left| A \right|}\] \[\Rightarrow \]If \[\left| A \right|=0\], then \[{{A}^{-1}}\]does not exist \[\therefore \]Reason \[\left| A \right|=0\]is not valid for given Assertion \[\therefore \]A is true but R is false Hence option [C] is the correct answer.
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