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

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

# Parents

* Nonsingular matrices and equivalences