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Letbe the real field andbe the set of all  m  ×  n  matrices overwhereFor a square matrixdenotes the trace of  A  (the sum of all diagonal entries of  A ). The symmetry trace graphofis defined to be a graph with vertex set of all nonzero matrices inand two vertices  A  and  B  are adjacent if and only ifwhereis the transpose of  B . Clearly,is undirected and without loops. In the present paper, by studying maximum cliques ofwe determine the form of an arbitrary automorphism of

Automorphism group of the symmetry trace graph of real matrices