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Study the Assertion and Reason and choose the correct option.
If A is a skew-symmetric matrix of order 3 × 3, then det(A) = 0.
Assertion: If $A$ is a skew-symmetric matrix of order $3 \times 3$, then $\det(A) = 0$.
Reason: If $A$ is a square matrix, then $\det(A) = \det(A')$.
- (a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
- (b)Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
- (c)Assertion is true and Reason is false.
- (d)Assertion is false and Reason is true.
Answer
Answer
Correct option: (a)
Answer: (a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
Reason is true. For skew-symmetric $A$, $A'=-A$, so $\det(A)=\det(A')=\det(-A)=(-1)^3\det(A)=-\det(A)$. Hence $2\det(A)=0$, so $\det(A)=0$: the Assertion is true and follows from the Reason.