Consider the modular number system $N=(Z_9,),$ where $$ is the multiply operator

defined in $Z_9.$

$($a$)(5$ points$)$ List all the numbers in $Z_9,$ which have multiplicative inverse in $Z_9.$

$($b$)(10$ points$)$ Create a multiply table of the numbers in the list found in $($a$).$

$($c$)(5$ points$)$ Using the multiply table in $($b$),$ find the multiplicative inverse for

each number in the list found in $($a$).$