Question

Assertion $\left(A\right)$:
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 $\left(R\right)$:
A square matrix $A=a_{ij}$ of order $m$ is said to be skew symmetric if $A^T=-A$.

• A. Both $\left(A\right)$ and $\left(R\right)$ individually true and $\left(R\right)$ is correct explanation of $\left(A\right)$
• B. Both $\left(A\right)$ and $\left(R\right)$ individually true but $\left(R\right)$ is not the correct explanation of $\left(A\right)$
• C. $\left(A\right)$ is true but $\left(R\right)$ is false
• D. $\left(A\right)$ is false but $\left(R\right)$ is true

Answer 1

The correct option is A Both $\left(A\right)$ and $\left(R\right)$ individually true and $\left(R\right)$ is correct explanation of $\left(A\right)$

$A=\left[\begin{array}{ccc}0& a& b\\ -a& 0& c\\ -b& -c& 0\end{array}\right]\therefore A^T=\left[\begin{array}{ccc}0& -a& -b\\ a& 0& -c\\ b& c& 0\end{array}\right]$
$\Rightarrow A^T=-A$
$\Rightarrow A$ is a skew-symmetric matrix.
$\therefore$ Asseration $\left(A\right)$ and Reason $\left(R\right)$ both are true and $\left(R\right)$ is correct explanation of $\left(A\right)$.