SymmetricMatrixQ
SymmetricMatrixQ[m] gives True if m is explicitly symmetric, and False otherwise.
Examples
Test for symmetric matrix:
SymmetricMatrixQ[{{1, 2}, {2, 3}}]
(* True *)Non-symmetric matrix:
SymmetricMatrixQ[{{1, 2}, {3, 4}}]
(* False *)Please visit the official Wolfram Language Reference for more details.