Quaternions are a number system that extends to complex numbers discovered by william hamilton in 1843.
multiplication of quaternions is not commutative and is defined as the quotient of two vectors. they are useful in
three-dimensional rotation calculations for computer graphics. quaternions are formed the following way:
i2 = = k2 = iii = −1
multiplication by −1 and 1 works normally. we can represent all possible multiplications of quaternions through a
table:
× i k
i −1 k −
−k −1 i
k −i −1
a. is multiplication of quaternions commutative? explain why or why not.
b. is multiplication of quaternions associative? explain why or why not.