# Equivalence theorem for nonsingular matrices: there is a pivot position in every row of A.

**Theorem:** An  	imes $n \times n$ matrix $A$ is nonsingular if and only if Thereiff there is a pivot position in every row of $A$. With $n$ pivots in an $n \times n$ matrix, the RREF is the identity, meaning $A$ is row-equivalent to $I$, hence nonsingular.

# Parents

* Nonsingular matrices and equivalences