Question

Assertion :Statement-1: Determinant of a skew-symmetric matrix of order 3 is zero. Reason: Statement-2: For any matrix A, $Det\left(A\right)=Det\left(A^T\right)$ and $Det(-A)=-Det\left(A\right)$ Where $Det\left(A\right)$ denotes the determinant of matrix A. Then,

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is C Assertion is correct but Reason is incorrect

Let A is a skew-symmetric matrix
$A^T=-A$
Taking determinant of (i), we get
$|A^T|=|-A|$
$|A|=(-1)|A|$ ($\because |A|=|A^T|$)
$\Rightarrow |A|=(-1{)}^n|A|$ where n is order of matrix
Since, $n=3$ is odd
$\Rightarrow |A|=-|A|$
$\Rightarrow 2|A|=0$
Therefore, statement 1 is true.
Hence, option 'C' is correct.
Statement 2 is incorrect $det\left(A\right)=-\left(detA\right)$ for odd order matrix only