| Assertion : \[\left| AA' \right|=0\] |
| Reason: A is skew matrix. |
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 \[\left| AA' \right|=0\Rightarrow \left| A \right|\,\,\left| A' \right|=0\] ...(1) |
| \[\Rightarrow \]either \[\left| A \right|\text{ }=\text{ }0\] or \[\left| A' \right|\text{ }=\text{ }0\] |
| Or |
| \[\left| A \right|=0\] and \[\left| A' \right|=0\] |
| We know that \[\left| A \right|=\left| A' \right|\] |
| \[\therefore \]from (1) \[\left| A \right|\,\,\,\left| A \right|=0\Rightarrow \,{{\left| A \right|}^{2}}=0\,\,\Rightarrow \left| A \right|=0\] |
| .'. Assertion is\[\left| A \right|=0\]. |
| Also Reason is A is skew symmetric matrix. |
| We know that \[\left| A \right|=0\], when order of skew matrix A is odd and \[\left| A \right|\ne 0\], when order of skew matrix is even |
| \[\therefore \]Assertion \[\left| A \right|=0\] is not valid for shew symmetric matrix of even order |
| \[\therefore \]Reasion : A is skew symmetric is not valid reason for Assertion : \[\left| AA' \right|=0\]. |
| A is true but R is false |
| Hence option [C] is the correct answer. |
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