a$)$Fill out the highlighted fields in the table below. What is the value of $n$ in $(Z_n,o+,ox)?$

b$)$Indicate whether $Z_n$ is a field. Explain the reason why by mentioning two important properties we can check from the chart below.

c$)$ What is the inverse of $7$ for addition if there exist an inverse?

d$)$ What is the inverse of $7$ for multiplication if there exist an inverse?

$\backslash$table$[[o+,0,1,2,3,4,5,6,7,8,9],[0,0,1,2,3,4,5,6,7,8,9],[1,1,2,3,4,5,6,7,8,9,0],[2,2,3,4,5,6,1,8,9,0,1],[3,3,4,5,6,7,8,9,0,1,2],[4,4,5,6,7,8,9,0,1,2,3],[5,5,6,7,8,9,0,1,2,3,4],[6,6,7,8,9,0,1,2,3,4,5],[7,7,8,9,0,1,2,3,4,5,6],[8,8,9,0,1,2,3,4,5,6,7],[9,9,0,1,2,3,4,5,6,7,8]]$

$\backslash$table$[[ox,0,1,2,3,4,5,6,7,8,9],[0,0,0,0,0,0,0,0,0,0,0],[1,0,1,2,3,4,5,6,7,8,9],[2,0,2,4,6,8,0,2,4,6,8],[3,0,3,6,9,2,5,8,1,4,7],[4,0,4,8,2,6,0,4,8,2,6],[5,0,5,0,5,0,5,0,5,0,5],[6,0,6,2,8,4,0,6,2,8,4],[7,0,7,4,1,8,5,2,9,6,3],[8,0,8,6,4,2,0,8,6,4,2],[9,0,9,8,7,6,5,4,3,2,1]]$