Let's say I have the field $F_{11}$. Why does $2$ have the multiplicative inverse $6$?
In some of the examples I have, let's say we are looking $F_5$, why are values up to only $2$ considered? So in the example of $F_5$, values $1$, $2$, then $-2$, $-1$ are considered. What about value of $2$ to $5$? And why do we consider negative values?
The same with $F_{13}$, why are values from $1$ to $6$ considered then $-6$ to $-1$?