If the matrix $\begin{bmatrix}a& -2 & 5b\\2 & 0 & -15\\15 & 3c & 0 \end{bmatrix}$ is skew-symmetric, then the value of $a^2+b^2+c^2 $ is :

34

The correct answer is Option (2) → 34

for a skew-symmetric matrix,

$A^T=-A$

$\begin{bmatrix}a& 2 & 15\\-2 & 0 & 3c\\5b & -15 & 0 \end{bmatrix}=\begin{bmatrix}-a& 2 & -5b\\-2 & 0 & 15\\-15 & -3c & 0 \end{bmatrix}$

$⇒a=-a=0$

$⇒-5b=15⇒b=-3$

$⇒3c=15⇒c=5$

$∴a^2+b^2+c^2=34$