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

**Theorem:** An  	imes $n \times n$ matrix $A$ is nonsingular if and only if The matrixiff $A$ has an inverse $A^{-1}$ satisfying $AA^{-1} = A^{-1}A = I$. This is the defining property of a nonsingular matrix.

# Parents

* Nonsingular matrices and equivalences