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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!