Question

The matrix $\left[\begin{array}{ccc}0& 5& -7\\ -5& 0& 11\\ 7& -11& 0\end{array}\right]$ is

• A. a skew-symmetric matrix
• B. a symmetric matrix
• C. a diagonal matrix
• D. an upper triangular matrix

Answer 1

Answer: (A)

Let $A=\left[\begin{array}{ccc}0& 5& -7\\ -5& 0& 11\\ 7& -11& 0\end{array}\right]$
$A^T=\left[\begin{array}{ccc}0& -5& 7\\ 5& 0& -11\\ -7& 11& 0\end{array}\right]=-\left[\begin{array}{ccc}0& 5& -7\\ -5& 0& 11\\ 7& -11& 0\end{array}\right]=-A$
$\therefore A^T=-A$
$\Rightarrow A$ is skew-symmetric matrix.