# Equivalence theorem for nonsingular matrices: the null space of the matrix A is {0}.

Put content here**Theorem:** An $n \times n$ matrix $A$ is nonsingular iff $\text{null}(A) = \{0\}$. The null space contains only the zero vector, meaning $Ax = 0$ has only the trivial solution.

# Parents

* Nonsingular matrices and equivalences