If $A=\begin{bmatrix}0 & 2 & c\\a & b & -1\\-5 & 1 &0\end{bmatrix}$ is a skew-symmetric matrix, then $(a+b+c)^3=$

27

$A=\begin{bmatrix}0&2&c\\a&b&-1\\-5&1&0\end{bmatrix}.$

$A \text{ is skew-symmetric } \Rightarrow a_{ij}=-a_{ji} \text{ and diagonal entries are }0.$

$b=0.$

$a=-2.$

$c=5.$

$a+b+c=-2+0+5=3.$

$(a+b+c)^3=3^3=27.$

$(a+b+c)^3=27.$