# Hamiltons quaternion rule states that ij=k and ji=-k. How can

Hamiltons quaternion rule states that ij=k and ji=-k. How can the commutative rule just be broken to make this true?
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jugf5
"Commutative rule" (as you call it) cannot be "broken," since it is a property that some operations have and some don't. Nothing here is "broken." Multiplication of quaternions is just not commutative (or, in other words, does not satisfy the commutative property).