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Let $A$ be an $n \times n$ matrix with $I_{n}$ the identity matrix. The statement det $A \neq 0$ is equivalent to:

A. All the given options are equivalent.

B. $A$ is row equivalent to $I_{n}$

C. $\operatorname{rank} A=n$

D. $A X=B$ is consistent for any $n \times 1$ matrix $B$

E. $A^{-1}$ exists
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