Hi all! I have two questions for y'all; talkin' bout Linear Algebra.

1) Explain why the columns of an n * n matrix A are linearly independent when A is invertible.

2) Suppose A in x * n and the equation Ax = 0 has only the trivial solution. Explain why A has n pivot columns and A is row equivalent to I(sub)n. This shows that A must be invertible.

Thanks sooo much guys!!! I really appreciate it! Linear Lolgebra ftl.