# Equivalence theorem for nonsingular matrices: the matrix A row-reduces to the identity matrix.

Put content here**Theorem:** An  	imes n$ matrix $ is nonsingular if and only if The matrix $A$ row-reduces to the identity matrix $I_n$. This means $A$ is a product of elementary matrices (each corresponding to a row operation), and products of invertible matrices are invertible.

# Parents

* Nonsingular matrices and equivalences