A square matrix is symmetric if each i, j entry equals the j, i entry, that is,

Question:

A square matrix is symmetric if each i, j entry equals the j, i entry, that is, if the matrix equals its transpose.
(a) Prove that for any square H, the matrix H + HT is symmetric. Does every symmetric matrix have this form?
(b) Prove that the set of n × n symmetric matrices is a subspace of Mn×n.