Quadratic matrix/Rank/Invertible/Linearly independent/Fact

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Let ${}K$ be a field, and let ${}M$ denote an ${}n\times n$ -matrix over ${}K$ . Then the following statements are equivalent.

${}M$ is invertible.
The rank of ${}M$ is ${}n$ .
The rows of ${}M$ are linearly independent.
The columns of ${}M$ are linearly independent.

Proof, Write another proof

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Mathematical fact