What is the characteristic of the ring of quaternions Solution Quaternions are a number system that extends to complex numbers Thus quaternions will have not only real numbers but also complex numbers. Normally the elements will be {-1,-i,-j,-k,1,i,j,k} with Cayley table as Multiplicative identity is 1. Additive identity =0 Characteristic is n such that 1+1+1+...+1 n times =0 (Since it is not possible to have as above, n is undefined.x1ijk11ijkii-1k-jjj-k-1ikkj-1-i.