Definition of nonsingular matrix: matrix is invertible
Definition: An $n \times n$ matrix $A$ is nonsingular (or invertible) if there exists a matrix $A^{-1}$ such that $AA^{-1} = A^{-1}A = I_n$.
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Definition: An $n \times n$ matrix $A$ is nonsingular (or invertible) if there exists a matrix $A^{-1}$ such that $AA^{-1} = A^{-1}A = I_n$.