| Assertion : If \[{{\left| A \right|}^{2}}=25\] then \[\left| A \right|=\pm \frac{1}{5}\] |
| Reason: \[\left| AB \right|=\left| A \right|\,\,\,\left| B \right|\] |
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 :
Given Assertion is \[\left| {{A}^{2}} \right|=25\Rightarrow \,\,\left| AA \right|=25\] \[\Rightarrow \,\,\,\left| A \right|\,\,\left| A \right|=25\,\,\Rightarrow \,{{\left| A \right|}^{2}}=25\,\,\Rightarrow \left| A \right|=\pm \,5\] \[\therefore \]Given Assertion [A] is false Also \[\left| AB \right|=\left| A \right|\,\,\,\left| B \right|\]{property of determinant}, \[\therefore \]Reason (R) is true. Hence option [D] is the correct answer.
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