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

Put content here**Theorem:** An $n \times n$ matrix $A$ is nonsingular iff $A^T$ has an inverse. Since $\det(A^T) = \det(A)$, $A^T$ is invertible iff $A$ is invertible. Moreover, $(A^T)^{-1} = (A^{-1})^T$.

# Parents

* Nonsingular matrices and equivalences