If the matrix $A=\begin{bmatrix}0 & 2 & c\\a & b & 1\\-3 & -1 & 0\end{bmatrix}$ is a skew-symmetric matrix, then a+ b + c is equal to :

1

The correct answer is option (3) → 1

$A=-A^T$ (skew symmetric)

$\begin{bmatrix}0&2&c\\a&b&1\\-3&-1&0\end{bmatrix}=-\begin{bmatrix}0&a&-3\\2&b&-1\\c&1&0\end{bmatrix}$

so $b=0$ (diagonal elements in skew symmetric matrix is zero)

$c=3$

$a=-2⇒(a+b+c)=1$