# Equivalence theorem for nonsingular matrices: the linear transformation given by T(x)=Ax has an inverse.

Put content here**Theorem:** An $n \times n$ matrix $A$ is nonsingular iff $T(x) = Ax$ has an inverse transformation $T^{-1}$. The inverse transformation is given by $T^{-1}(y) = A^{-1}y$.

# Parents

* Nonsingular matrices and equivalences