Question

Assertion :The determinant of a matrix $A=\left[\begin{array}{ccc}0& 1& 2\\ -1& 0& 3\\ -2& -3& 0\end{array}\right]$ is zero Reason: The determinant of every skew symmetric matrix of odd order is zero.

• 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),

$A=\left[\begin{array}{ccc}0& 1& 2\\ -1& 0& 3\\ -2& -3& 0\end{array}\right]$
$\therefore \left|A\right|=0$
$A^T=\left[\begin{array}{ccc}0& -1& -2\\ 1& 0& -3\\ 2& 3& 0\end{array}\right]=-\left[\begin{array}{ccc}0& 1& 2\\ -1& 0& 3\\ -2& -3& 0\end{array}\right]$
$A^T=-A$
$\therefore$ Matrix A is, skew symmetric matrix, of odd order
Assertion (A) & Reason (R) both are individually true & Reason (R) is the correct explanation of Assertion (A)
Hence, option A.