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

Put content here**Theorem:** An  	imes n$ matrix $ is nonsingular if and only if The matrix $A$ 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