1. The problem statement, all variables and given/known data In the Pauli theory of the electron, one encounters the expresion: (p - eA)X(p - eA)ψ where ψ is a scalar function, and A is the magnetic vector potential related to the magnetic induction B by B = ∇XA. Given that p = -i∇, show that this expression reduces to ieBψ. 2. Relevant equations 3. The attempt at a solution I'm first working this matrix determinant out without substitution, although I know the answer should include the B vector, and look something like this: ieBψ I split (p - eA) into its vector components and used the determinant, but it's just getting messy and I don't know what to do. My first question is, do I need to work this matrix out or is there an identity I should use to avoid all this? I've done this problem almost 10 times by brute force and can't seem to get it. This problem has been asked about previously but it wouldn't let me re-open the thread.