If $\left[\begin{array}{ccc}0 & a+3 b & -7 \\ -1 & 0 & 3 a+b \\ 7 & -11 & 0\end{array}\right]$ is a skew-symmetric matrix, then $2 a-8 b$ is equal to:

16

The correct answer is Option (3) → 16

$A=\begin{bmatrix}0 & a+3b & -7 \\ -1 & 0 & 3a+b \\ 7 & -11 & 0 \end{bmatrix}$

$\text{Skew-symmetric} \Rightarrow A^T=-A$

$a+3b = 1$

$3a+b = 11$

$3(a+3b)=3 \Rightarrow 3a+9b=3$

$(3a+9b)-(3a+b)=3-11$

$8b=-8 \Rightarrow b=-1$

$a+3(-1)=1 \Rightarrow a=4$

$2a-8b=2(4)-8(-1)=8+8=16$

$2a-8b=16$