Let c be in a ring R and let I = {rc | r is in R}

Give an example to show that if R is not a commutative ring, then I need not be an ideal.

Can someone help me this? I think the best ring to represent R is the 2 by 2 matrix, since it's not commutative. But I already tried few particular matrix, but I couldn't find the one that satisfies the given condition. Appreciate someone's help. Thanks...