Why if $det(a) \ne 0$ then rows are linearly independent?

Question

Why if $det(a) \ne 0$ then rows are linearly independent? Trying find it in internet, but only found facts.

It depends on your definition of determinant. There are many, all equivalent, but you might be confused to see different definitions. Please, what is your definition of the determinant? — Crostul, Mar 01 '17 at 10:36
Do you own a linear algebra textbook? I think that would be a better place to look. — Hans Lundmark, Mar 01 '17 at 21:20

score 1 · Accepted Answer · answered Mar 01 '17 at 10:37

One way to look at it:

For a set of vectors forming a square matrix, to have $\det\neq 0$ means that this matrix is invertible. If the square matrix formed by your set of vectors is invertible, then you can transform this matrix into the identity matrix performing elementary row operations on it. This means that the vectors in the original matrix are linearly independent.

Why if $det(a) \ne 0$ then rows are linearly independent?

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