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
A skew symmetric matrix satisfies \(A^T = -A\), that is \(a_{ij} = -a_{ji}\). In particular every diagonal entry is 0.
\(a_{33} = c = 0\)
\(a_{12} = -a_{21}:\quad a = -(-2) = 2\)
\(a_{23} = -a_{32}:\quad b = -2\)
The remaining pair also fits: \(a_{13} = 2 = -a_{31}\).
\(a + b + c = 2 - 2 + 0 = 0\)
\((a + b + c)^3 = 0\)