| Assertion [A]: For a square matrix\[A,\,{{\left( 2A \right)}^{-1}}=\frac{1}{2}{{A}^{-1}}\]. |
| Reason [R]: For any matrix A and scalar k, kA is a matrix obtained by multiplying each element of A by k. |
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: D
Solution :
We know that, \[{{\left( kA \right)}^{-1}}\ne \frac{1}{k}\left( {{A}^{-1}} \right)\] \[\therefore \]Given Assertion is not true Clearly Reason R is true \[\therefore \]A is false and R is true Hence option [D] is the correct answer.
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