Question

Assertion :If $A$ is skew symmetric matrix of order $3\times 3$, then $det\left(A\right)=0$ or $\left|A\right|=0$ Reason: If $A$ is a square matrix, then $det\left(A\right)=det\left(A\right){}^{\prime }=det\left({-A}^{{}^{\prime }}\right)$

• 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

Assertion:

For a skew symmetric matrix

$\left|\begin{array}{ccc}0& -a& -b\\ a& 0& -c\\ b& c& 0\end{array}\right|$

$△=0$

Assertion is true

Reason:

$det\left(A\right)=det{\left(A\right)}^T=det(-A^T)\to$

But

$det\left(A\right)=det{\left(A\right)}^T=det\left(A^T\right)\to$

Hence Reason is false