If \( A=\begin{bmatrix}0 & a & 1\\-1 & b & 1\\-1 & c & 0\end{bmatrix} \) is a skew symmetric matrix, then the value of \( (a+b-c)^{2} \) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 4
A is skew symmetric when \( a_{ij}=-a_{ji} \) for all i, j; in particular every diagonal element is 0.
\( \displaystyle a_{12}=-a_{21}\ \Rightarrow\ a=-(-1)=1 \)
\( \displaystyle a_{22}=0\ \Rightarrow\ b=0 \)
\( \displaystyle a_{32}=-a_{23}\ \Rightarrow\ c=-1 \)
\( \displaystyle (a+b-c)^2=(1+0+1)^2 \)
\( \displaystyle =4 \)