1. The problem statement, all variables and given/known data Prove that the following are equivalent: 1. N(A)=0 2. A is nonsingular 3. Ax=b has a unique solution for each b that exists in R^n. 2. Relevant equations 3. The attempt at a solution I think you prove this by showing that 1 implies 2, 2 implies 3, & 3 implies 1. But after that I don't know how to prove that.