There exists a matrix K ∈M₂(C) such that ∅ : H → M₂(C) defined by

for all a, b, c, d ∈ R, gives an isomorphism of H with ∅[H] 

a. Find the matrix K. 

b. What other thing should you check to show that ∅ gives an isomorphism of H with ∅ [H]?

0 = a[bi] + b[_id]+c[i b]+dk, p(a + bi+cj+dk) :