If $A = \begin{bmatrix} a & c & -1 \\ b & 0 & 5 \\ 1 & -5 & 0 \end{bmatrix}$ is a skew-symmetric matrix, then the value of $2a - (b + c)$ is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0 ##
We know that, if matrix $A$ is skew symmetric, then
$A = -A'$
$∴\begin{bmatrix} a & b & 1 \\ c & 0 & -5 \\ -1 & 5 & 0 \end{bmatrix} = \begin{bmatrix} -a & -c & 1 \\ -b & 0 & -5 \\ -1 & 5 & 0 \end{bmatrix}$
On comparing matrices, we get
$a = -a \Rightarrow 2a = 0 \Rightarrow a = 0$
$b = -c$ and $c = -b$
Now, $2a + (b + c) = 2 \times 0 + (b - b) = 0$