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
Answer & explanation
Correct answer: option 2
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: $a + b + c = 2 + (-2) + 0 = 0$
$(a + b + c)^3 = 0^3 = 0$