Symmetric and skew symmetric matrices

Symmetric matrix

A square matrix is called a symmetric matrix iff a_ij = a_ji for all I,j.
It means (A)_ij = (A^T) _ij

skew symmetric matrix
A square matrix is called a skew-symmetric matrix iff a_ij = -a_ji for all I,j.
It means (A)_ij = -(A^T) _ij
It means A^T = -A