{1,4,7,13}multiplication mod 15 is closed? What is the meaning of {1,4 ,7,13}*15 I think the inverse of 4 is how many times we multiply 4 into 4 and devide by 15 such that remainder is 1.is this correct? But how the set is closed
2026-05-06 03:10:07.1778037007
How to know under multiplication modulo operation the set is closed or not
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"Closed" in this context means that it is closed under the operation of multiplication mod $15$. So for any $a,b \in \{1,4,7,13\}$, $ab$ reduced mod $15$ (which is indeed the remainder of division by $15$) is in $\{1,4,7,13\}$. Now, lets refer to this operation of multiplication mod $15$ with the symbol $*$.
The inverse of $4$ would be the number $a \in \{1,4,7,13\}$ such that $4*a = 1$. The same goes for the other elements.