AntisymmetricMatrixQ
AntisymmetricMatrixQ[m] gives True if m is explicitly antisymmetric, and False otherwise.
Examples
Test if a matrix is antisymmetric:
AntisymmetricMatrixQ[{{0, 1}, {-1, 0}}]
(* True *)A symmetric matrix is not antisymmetric:
AntisymmetricMatrixQ[{{1, 2}, {2, 1}}]
(* False *)Please visit the official Wolfram Language Reference for more details.