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If the linear combination x -> Ax maps R^{n}into R^{n}, then the row reduced echelon form of A is I.

I don't understand why this is False. My book says it is false because it is only true if it maps R^{n}ONTO R^{n}instead of R^{n}INTO R^{n}. What difference does the word into make?

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# Invertible Matrix Theorem

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