please help me with these T/F questions

Hint:

Zn = {0, 1, 2,... n-1}

Z_n* = {a in Zn : gcd(a,N) = 1}

1. For any n and g, if g is a generator of Z_n*, then g is invertible (mod n).
2. For any integers n and g,h in Z_n, if g and h are generators of Z_n*, then their productg*h is invertible (mod n)
3. For any integers n and g,h in Z_n, if g and h are invertible (mod n), then their product g*h is invertible (mod n)
4. For any prime p and g in Z_p, if g is not 0, then g is invertible (mod p)
5. For any integers n and g,h in Zn, if g and h are generators of Z_n*, then their sum g+h is also a generator of Z_n*.
6. For any integers n and g,h in Zn, if g and h are generators of Zn*, then their product g*h is also a generator of Z_n*.
7. For any integer n and g in Z_n, if g is not 0, then g is invertible (mod n)
8. For any n and g, if g is invertible (mod n), then g is a generator of Z_n*
9. For any integers n and g,h in Z_n, if g and h are invertible (mod n), then their sum g+h is invertible (mod n)
10. For any integers n and g,h in Z_n, if g and h are generators of Z_n*, then their sum g+h is invertible (mod n)