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

1

The correct answer is Option (1) → 1 ##

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

When the matrix $A$ is skew-symmetric, then

$A = -A^T$

$\Rightarrow a_{ij} = -a_{ji}$

$\Rightarrow c = -2; \ a = 0 \text{ and } b = 3$

So, $a + b + c = 0 + 3 - 2 = 1$.