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

0

The correct answer is Option (2) → 0

For a skew symmetric matrix $A$, we have $A^T = -A$ and all diagonal elements are 0.

Given matrix:

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

Since $A$ is skew symmetric:

- Diagonal elements: $0, 0, 0 \Rightarrow c = 0$

- Off-diagonal elements satisfy $a_{ij} = -a_{ji}$:

$a = -(-2) = 2$

$b = -2$

Sum: $a + b + c = 2 + (-2) + 0 = 0$

$(a + b + c)^3 = 0^3 = 0$