If \(A = \begin{bmatrix} 0 & 2 & c \\ a & b & -1 \\ -5 & 1 & 0 \end{bmatrix}\) is a skew-symmetric matrix, then \((a + b + c)^3 =\)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 27
In a skew-symmetric matrix, \(a_{ij} = -a_{ji}\); in particular every diagonal element is 0.
\(b = a_{22} = 0\)
\(a = a_{21} = -a_{12} = -2\)
\(c = a_{13} = -a_{31} = 5\)
(The remaining pair agrees: \(a_{23} = -1 = -a_{32}\).)
\(a + b + c = -2 + 0 + 5 = 3\)
\((a + b + c)^3 = 27\)