If A is a nonsingular matrix, what is the null space of A?

Question

If A is nonsingular then the equation:

A x = y

has a unique solution. Now, the equation:

A x = 0

always has a solution:

x = 0.

If A is nonsingular, then this must thus be the only solution. This means that the null space of A is the zero dimensional vector space containing only the null vector 0.