If $A=\begin{bmatrix}a&4&-5\\d&b&-6\\5&e&c\end{bmatrix}$ is a skew symmetric matrix, then value of $a + b + c + d + e$ is equal to

2

The correct answer is Option (4) → 2

$A=\begin{bmatrix} a & 4 & -5 \\ d & b & -6 \\ 5 & e & c \end{bmatrix}$ is skew symmetric

For skew symmetric matrix,

$A^T=-A$

So diagonal entries are zero,

$a=0,b=0,c=0$

Also,

$d=-4$

$e=6$

Now,

$a+b+c+d+e=0+0+0-4+6$

$=2$