The quaternions are expressions of the form $\displaystyle a+bi+cj+dk$, where $\displaystyle a;b;c;d$ are

real numbers. They are added by the “obvious rule”, and multiplication is based on the formulae:

$\displaystyle i^2 = j^2 = k^2 = ijk = -1$:

(a) Prove that the associative law for multiplication holds.

(b) Prove that the distributive law holds.

(c) Prove that the commutative law for multiplication does not hold.[/tex]

How would I prove these?