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

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

# Parents

* Nonsingular matrices and equivalences