| Assertion [A]: For a matrix \[A={{\left[ {{a}_{ij}} \right]}_{3}}\], if det. (adj A) = 49 then det\[\left( A \right)\text{ }=\text{ }\pm 7\]. |
| Reason [R]: For a square matrix A of order n, \[\left| adj\,\,A \right|={{\left| A \right|}^{n-1}}\]. |
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: A
Solution :
Given \[\det \left( adj\,\,A \right)=49\] \[\Rightarrow \,\,\,{{\left| A \right|}^{2}}=49\,\,\Rightarrow \left| A \right|=\pm 7\] \[\therefore \]Given Assertion [A] is true Also we know that For a square matrix of order \[n\,\,\left| adj\,\,A \right|\,\,={{A}^{n-1}}\] \[\therefore \]For \[n=3\], \[\left| adj\,\,A \right|={{A}^{2}}\] \[\therefore \]Given Reason is true and is valid explanation for given Assertion. Hence option [A] is the correct answer.
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