Question

Find the transpose of $A$ and state whether it is a symmetric, a skew-symmetric or neither. $A=\left[\begin{array}{ccc}2& 5& 1\\ -5& 4& 6\\ -1& -6& 3\end{array}\right]$

Answer 1

Let $A=\left[\begin{array}{ccc}2& 5& 1\\ -5& 4& 6\\ -1& -6& 3\end{array}\right]$

$A=\left[\begin{array}{ccc}-2& -5& -1\\ 5& -4& -6\\ 1& 6& -3\end{array}\right]$

$A^T=\left[\begin{array}{ccc}2& -5& -1\\ 5& 4& -6\\ 1& 6& 3\end{array}\right]$

$A\ne A^T$ as well as $-A\ne A^T$

Hence the given matrix is neither symmetric, nor skew-symmetric matrix.