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

Put content here**Theorem:** An  	imes n$ matrix $ is nonsingular if and only if 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