We can ask how the matrix product operation interacts with the transpose operation. (a) Show that (GH)T

Question:

We can ask how the matrix product operation interacts with the transpose operation.
(a) Show that (GH)T = HTGT.
(b) A square matrix is symmetric if each i, j entry equals the j, i entry, that is, if the matrix equals its own transpose. Show that the matrices HHT and HTH are symmetric.