Hi, i'm finding the following question difficult;

Let R be a ring with a one. Show that if 1=0 in R (i.e 1_R=0_R) then 0 is the only element in R , so that R is the zero ring.

Also in Z_10 is it right that the units are 1, 3, 7 and 9 with inverses 1, 7, 3, 9, respectively?

Thanks for your help!