Commutative means that changing the order of the operands yields the same result. Ex: a+b = b+a. In that way, "alternative" is (mostly) commutative, but there are exceptions: Amazon is an alternative to a local bookstore, but a local bookstore is not necessary an alternative to Amazon.

The transitive property implies that if a=b and b=c, then a=c. "Alternatives" are also (mostly) transitive. A counterexample would be that Slack is an alternative to IRC, and IRC is an alternative to Slack, but Slack is not an alternative to Slack!