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# Equivalence theorem for nonsingular matrices: the nullity of the matrix A is 0.

Put content here**Theorem:** An $n \times n$ matrix $A$ is nonsingular iff $\text{nullity}(A) = 0$. By the rank-nullity theorem, $\text{rank}(A) + \text{nullity}(A) = n$, so nullity 0 means rank $n$.

# Parents

* Nonsingular matrices and equivalences