4.
Let A,B be aritrary matrices whose product exists.

Show that AA^ and A^A exist and Hermitian (^ represent complex conjugate)
Show that the product (B^A^) exists and equal to (AB)^
If both A and B are Hermitian, show that AB+BA is Hermitian as well
If A and B are both Hermitian, show that (i(AB-BA) is Hermitian as well.

5.
show that each of the Pauli spin matrices is both Hermitian and unitary. Calculate teh inverse of each.
Show that the product of two Pauli matrices is (see file for complete formulation)

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