I need help with this question, i want to know the exact method of doing it with explanation. i am not able to get around with the logic of it.
2026-03-31 07:52:34.1774943554
How to check field axioms given addition and multiplication tables
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For the multiplication table, take a look at what happens when you multiply $x$ with itself. Why is that a problem?
As for the method of doing it -- I just remembered what a field is defined to be: a commutative ring with a multiplicative identity, no zero divisors, and every element has a multiplicative inverse. There are actually multiple reasons why this is not a field. Take a look at the $x$ row in the multiplication table. Do you see any $1$s belonging to that row? No. Why is that a problem?