The Extended Euclidean Algorithm is used to compute gcd of r$0$ and

r$1$ in the form:

gcd$($r$0,$ r$1)=$ s $$ r$0+$ t $$ r$1$

Assume r$0,$ r$1,$ s$,$ t in Z

Show that if gcd$($r$0,$ r$1)=1,$ then r$1$ has a multiplicative inverse in mod$($r$0).$

What is the inverse?