Question

The matrix $A=\left[\begin{array}{ccc}0& 1& -1\\ -1& 0& 1\\ 1& -1& 0\end{array}\right]$ is a :

• A. Diagonal matrix
• B. Symmetric matrix
• C. Skew-symmetric matrix
• D. Identity matrix

Answer 1

The correct option is C Skew-symmetric matrix

The matrix $A=\left[\begin{array}{ccc}0& 1& -1\\ -1& 0& 1\\ 1& -1& 0\end{array}\right]$ is a $A^T=\left[\begin{array}{ccc}0& -1& 1\\ 1& 0& -1\\ -1& 1& 0\end{array}\right]$ $Hence{-A}^T=\left[\begin{array}{ccc}0& 1& -1\\ -1& 0& 1\\ 1& -1& 0\end{array}\right]A={-A}^T$
The matrix A is skew symmetric matrix