[math-fun] quaternion identity

Has anyone seen this somewhere? Quaternions a,b,c,d: abcd+acdb+adbc+badc+bcad+bdca+cabd+cbda+cdab+dacb+dbac+dcba = abdc+acbd+adcb+bacd+bcda+bdac+cadb+cbad+cdba+dabc+dbca+dcab The LHS is even permutations of abcd; RHS is odd. It should also work for 2x2 matrices of real or complex numbers. Rich