Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2005 / Paper 1 / 2 / a

True. The symmetric and antisymmetric parts of a matrix are, in Einstein summation convention,They satisfy $S_{ji}=S_{ij}$, $A_{ji}=-A_{ij}$ and $S_{ij}+A_{ij}=M_{ij}$. This works over the real or complex numbers; it uses division by two.