| Assertion: \[\left| P \right|=O\] |
| Reason : Determinant of skew symmetric matrix is O. |
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 \[\left| P \right|=O\Rightarrow \left| P' \right|=O\] |
| \[\left( \because \,\,\left| A \right|=\left| A' \right| \right)\] |
| Also for skew symmetric matrix \[A'=-A\] |
| \[\therefore \,\,\,\left| A' \right|=\det \left( -A \right)={{\left( -1 \right)}^{n}}\,\det \,\,A\] |
| If n is even, then \[\left| A' \right|=\left| A \right|\] |
| If n is odd, then \[\left| A' \right|=-\left| A \right|\] |
| \[\Rightarrow \,\,\left| A \right|=-\left| A \right|\Rightarrow 2\left| A \right|=0\Rightarrow \left| A \right|=0\] |
| \[\therefore \,\,\,\left| A \right|=0\]is possible when n is odd |
| \[\therefore \]Given Reason (R) is not valid for Assertion [A] |
| \[\therefore \]Assertion is true but Reason is false |
| Hence option [C] is the correct answer. |
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