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## Homework Statement:

- For n*n matrix, I would like to know how matrix A being invertible means that det(A) is not 0, that A is linearly independent, and that columns of A spans the matrix.

## Relevant Equations:

- NA

I have a trouble showing proofs for matrix problems. I would like to know how

A is invertible -> det(A) not 0 -> A is linearly independent -> Column of A spans the matrix

holds for square matrix A. It would be great if you can show how one leads to another with examples! :)

Thanks for helping out.

A is invertible -> det(A) not 0 -> A is linearly independent -> Column of A spans the matrix

holds for square matrix A. It would be great if you can show how one leads to another with examples! :)

Thanks for helping out.