Question

Assertion :The matrix $A=\left(\begin{array}{ccc}0& a& b\\ -a& 0& c\\ -b& -c& 0\end{array}\right)$ is a skew symmetric matrix. Reason: A square matrix $A=\left(a_{ij}\right)$ of order m is said to be skew symmetric if $A^T=-A$. .

• A. Both (A) & (R) are individually true & (R) is correct explanation of (A),
• B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).
• C. (A)is true but (R} is false,
• D. (A)is false but (R} is true.

Answer 1

The correct option is A Both (A) & (R) are individually true & (R) is correct explanation of (A),

$A=\left(\begin{array}{ccc}0& a& b\\ -a& 0& c\\ -b& -c& 0\end{array}\right)$
$\therefore A^T=\left(\begin{array}{ccc}0& -a& -b\\ a& 0& -c\\ b& c& 0\end{array}\right)$
$A^T=-A$
$\therefore$ Assertion (A) & Reason (R) both are true & Reason(R) is correct explanation of Assertion (A).