# Equivalence theorem for nonsingular matrices: the matrix A has a left inverse.

Put content here**Theorem:** An  	imes n$ matrix $ is nonsingular if and only if The matrix $A$ has a left inverse: there exists $B$ such that $BA = I$. For square matrices, a left inverse is also a right inverse, so $A$ is nonsingular.

# Parents

* Nonsingular matrices and equivalences