My other problem is: Consider now the space of 2x2 complex matrices. Show that the Pauli Matrices |I>= 1 0 0 1 |sigma x>= 0 1 1 0 |sigma y>= 0 -i i 0 |sigma z>= 1 0 0 -1 form an orthonormal basis for this space when k=1/2. To spare yourself from having to compute 10 different matrix products, I recommend that you write out what the inner product is for general matrices A and B first. I'm really lost on this one! Any help getting me started would be greatly appreciated!