Question

Out of the following which is a skew- symmetric matrix

• A. $\left[\begin{array}{ccc}0& 4& 5\\ -4& 0& -6\\ -5& 6& 0\end{array}\right]$
• B. $\left[\begin{array}{ccc}1& 4& 5\\ -4& 1& -6\\ -5& 6& 1\end{array}\right]$
• C. $\left[\begin{array}{ccc}1& 4& 5\\ -4& 2& -6\\ -5& 6& 3\end{array}\right]$
• D. $\left[\begin{array}{ccc}i+1& 4& 5\\ -4& i& -6\\ -5& 6& i\end{array}\right]$

Answer 1

The correct option is A $\left[\begin{array}{ccc}0& 4& 5\\ -4& 0& -6\\ -5& 6& 0\end{array}\right]$

In a skew-symmetrix matrix $a_{ij}=-a_{ji}\forall i,j=1,2,3forj=i,a_{ii}=-a_{ji}\Rightarrow$ each $a_{ii}=0$.
Hence the matrix $\left[\begin{array}{ccc}0& 4& 5\\ -4& 0& -6\\ -5& 6& 0\end{array}\right]$ is skew-symmetric.