Let n be a fixed positive integer greater than $1.$ If a mod n $5$ a$9$ and

b mod n $5$ b$9,$ prove that $($a $1$ b$)$ mod n $5($a$91$ b$9)$ mod n and $($ab$)$

mod n $5($a$9$b$9)$ mod n$.($This exercise is referred to in Chapters $6,$

$8,10,$ and $15.)$